DUDLEY  OBSERVATORY,  AT  ALBANY,  N 


POPULAR  ASTRONOMY. 


CONCISE    ELEMENTARY    TREATISE 


ON    THE 


SO,  PLANETS,  SATELLITES  A^7D  COMETS. 


BT 


0.  M.  MITCHEL,  LL.D., 

MUOTO*    Or     TUB     CINCINNATI     AND     DUDLEY     OB3UCY ATC SIM. 


NEW  YORK: 
OAKLEY    &    MASON", 

21    MURRAY    STREET. 


1866. 


A  T3  d  > 

Vwi  ';  V-,-  ^       ',._     - 


Entered,  according  to  Act  of  Congress,  in  the  year  1860,  by 

O.    M.    MITCHEL, 
la  the  Clerk's  Office  of  the  District  Court  for  the  Southern  District  of  New  Tort. 


BT 

SMITH     &    MoDOUGAL 
82  &  84  Beekman-st,  N.  Y. 


PREFACE. 


THE  author  has  no  other  apology  to  present  for  offer- 
ing to  the  public  the  following  work  on  "Popular 
Astronomy''  than  the  marked  favor  with  which  his 
"Planetary  and  Stellar  Worlds''  has  been  received,  both 
in  this  country  and  in  Europe. 

The  science  of  Astronomy  is  so  rapidly  progressive 
that  to  keep  the  public  advised  of  its  advances  new 
works  are  required  almost  every  year.  This  may  be 
offered  as  an  additional  reason  for  the  present  publica- 
tion. 

In  the  preparation  of  the  work  I  have  availed  myself 
of  so  many  sources  of  information  that  it  would  be  quite 
impossible  for  me  to  specify  the  authors  or  the  volumes 
to  which  I  am  indebted.  The  plan  and  the  cast  are  all 
my  own.  I  have  endeavored  to  follow  the  path  of  real 
discovery,  and  in  every  instance  to  present  the  facts  and 
phenomena  so  as  to  afford  to  the  reader  and  student  an 
opportunity  to  exercise  his  own  genius  in  their  discussion 

7073 


IV  PREFACE. 

and  resolution,  before  offering  the  explanation  reached  by 
ancient  or  modern  science.  It  is  hoped  that  this  method 
of  treating  the  subject  which  is  new,  (so  far  a3  I  know,) 
may  avail  in  exciting  a  greater  interest  in  the  examination 
of  those  great  problems  of  the  universe  whose  successfii 
solution  constitutes  the  chief  honor  of  human  genius. 

In  a  few  instances  I  have  ventured  to  present  tho 
results  of  my  own  observations,  and  have  occupied  a 
short  space  in  exhibiting  a  sketch  of  new  methods  and 
new  instruments,  which  have  been  introduced  into  the 
observatories  at  Cincinnati  and  at  Albany. 

On  page  376  will  be  found  a  note  addressed  to  those 
who  may  use  this  volume  as  a  class-book. 

DUDLEY  OBSERVATORY,  January,  186C. 


CONTENTS 


CHAPTER  I. 

THE  SUN,  THE  CENTRAL  ORB  OP  THE  PLANETARt  SYSTEM. 

PAAV 

OMCOVICRIES  OF  THIS  ANCIENTS. — The  Source  of  Light  and  Heat  and  Life* — The 
Ban's  apparent  Motion.— Length  of  the  Year.— The  Sun's  apparent  Path 
among  the  Fixed  Stars,  a  Circle. — His  apparent  Motion  not  Uniform. — The 
Explanation  of  Hipparchus.— Solar  Eclipses.— Their  Prediction. 

Disco  VERIKS  OF  THE  MODERNS.— The  Sun^s  Distance.— His  Horizontal  Paral- 
lax.— Importance  of  this  Element— Measured  by  the  Transit  of  Venus.— 
The  Sun  s  real  Magnitude,  ami  Microraetrical  Measure  of  his  Diameter.— 
The  Physical  Constitution  of  the  Sun.— Solar  Spots.— Their  Periodicity.— 
Hypotheses  and  Speculations. 18 

CHAPTER   II. 

MERCURY,   THE  FIRST  PLANET  IN  THE    ORDER  OF  DISTANCE 
FROM  THE  SUN. 

Its  Early  Discovery.— Difficult  to  be  distinguished  from  the  Stars.— Elonga- 
tions.— Motion  Direct  and  Retrograde. — Sometimes  Stationary. — Nature  of 
the  Orbit— Variation  in  the  Elongation  Explained.— The  Nodes.— Transit  of 
Mercury.— Inclination  of  Mercury  s  Orbit— Mean  Distance  from  the  Sun.— 
Conjunctions. — Phases. — Diameter  and  Volume 4b 

CHAPTER  III. 

VENUS,  THE  SECOND  PLANET  IN  THE  ORDER  OF  DISTANCE  FROM 
THE  SUN. 

The  First  Planet  Discovered.— Mode  of  Its  Discovery.— Her  Elongations.— 
Morning  and  Evening  Star. — A  Sattellite  of  the  Sun. — Her  superior  and  In- 
ferior Conjunctions.— Her  Stations.— Direct  and  Retrograde  Motions.— These 
Phenomena  indicate  a  Motion  of  the  Earth. — Transits  of  Venus. — Inclina- 
tion of  the  Orbit  of  Venus  to  the  Ecliptic. — Her  Nodes. — Intervals  of  her 
Transits.— Knowledge  of  the  Ancients.— Phases  of  Venus.— Her  Elongations 
Unequal.— No  Sattellite  yet  Discovered.— Sun's  Light  and  Heat  at  Venus. — 
Her  Atmosphere &f 

CHAPTER    IV. 

THE  EARTH  AND  ITS  SATTELLITE;   THE  THIRD  PLANET  IN  THE 
ORDER  OF  DISTANCE  FROM  THE  SUN. 

The  Earth  the  apparent  Center  of  Motion.— To  all  the  Senses  it  is  at  Rest— 
The  Center  of  the  Motions  of  the  Sun  and  Moon. — Explanation  of  the  Ac- 
celeration of  the  Orbitual  Motion  of  the  Sun  and  Moon. — Ptolemy's  Epicy- 
cles.—The  Explanation  of  Copernicus.— The  Sun  the  Center  of  Planetary 
Motion.— The  Earth  One  of  the  Planets.— Objections  to  this  Hypothesis.— 
The  Answer. — System  of  Jupiter  discovered  by  the  Telescope. — The  Old  Sys- 
tem superseded  by  the  New.— The  Figure  and  Magnitude  of  the  Earth 

How  determined.— The  Earth's  Motions.— Rotation  and  Revolution.— A 
Unit  of  Time  furnished  by  the  Earth's  Period  of  Rotation.— Earth's  Orbit- 
nal  Motion.— Vernal  Equinox.— Perihelion  of  Earth's  Orbit— Its  Period  of 
Revolution.— Solar  and  Sidereal  Time. 

THK  MOON.— Revolution  in  her  Orbit— Her  Phases.— Eccentricity  of  her  Or- 
bit— Revolution  of  her  Apogee. — Inclination  of  her  Oibit — Moon's  Paral- 
lax and  Distance.— Her  Physical  Constitution.— Center  of  Gravity  and  Cen- 
ter of  Figure. 89 


VI  CONTENTS. 


CHAPTER  V. 

MAES,  THE  FOUKTH  PLANET  IN  THE  ORDER  OF  DISTANCE  FROM 
THE  SUN. 

PAOI 

Phenomena  of  Mars  difficult  to  explain  with  the  Earth  as  tho  Center  of  Mo- 
tion.— Copernican  system  applied. — Epicycle  of  Mars. — Better  Instruments 
and  more  accurate  Observations. — Tycho  and  Kepler. — Kepler's  method  of 
Investigation.— Circles  and  Epicycles  exhausted.— The  Ellipse.— Its  Proper- 
ties.—The  Orbit  of  Mars  an  Ellipse.— Kepler's  Laws.— Elliptical  Orbits  of 
the  Planets.— The  Elements  of  the  Planetary  Orbits  explained— How  these 
Elements  are  obtained.— Kepler's  third  Law.— Value  of  this  Law.— The  Phys- 
ical Aspect  of  Mars. — Snow  Zones. — Kotation  of  the  Planet. — Diameter  and 
Volume. — Speculation  as  to  its  Climate  and  Color. 101 


CHAPTER   VI. 

THE  ASTEROIDS:   A  GROUP  OF  SMALL  PLANETS,    THE  FIFTH  IN  THE 
ORDER   OF  DISTANCE   FROM   THE   SUN. 

The  Interplanetary  Spaces. — Kepler's  Speculations. — Great  Interval  between 
Mars  and  Jupiter. — Bode's  Empirical  Law. — Conviction  that  a  Planet  exist- 
ed between  Mars  and  Jupiter. — Congress  of  Astronomers. — An  Association 
Organized  to  Search  for  the  Planet.— Discovery  of  Ceres. — Lost  in  the  Solar 
Beams. — Rediscovered  by  Gauss. — The  New  Order  Disturbed  by  the  Dis- 
covery of  Pallas.— Olber's  Hypothesis. — Discovery  of  Juno  and  Vesta. — The 
Search  Ceases. — Renewed  in  1846. — Many  Asteroids  discovered. — Their  Mag- 
nitude, Size,  and  probable  .Number ..  126 


CHAPTER   VII. 

JUPITER,   ATTENDED  BY  FOUR  MOONS,   THE   SIXTH  PLANET  IN  THE 
ORDER  OF  DISTANCE  FROM  THE  SUN.     ' 

Arc  of  Retrogradatlon. — Stationary  Point. — Distance  of  the  Planet  Determined. 
— Periodic  Time. — Synodical  Revolution  gives  the  Sidereal. — Surface  of  Ju- 
piter as  given  by  the  Telescope  —Period  of  Rotation. — Diameter. — Volume. 
— Mean  Distance.— Amount  of  Light  and  Heat. — Figure  of  Jupiter. — Equa- 
torial and  Poiar  Diameters. — Discovery  of  the  Four  Moons  by  Galileo. — Ef- 
fect on  the  Copernican  Theory  — Jupiter's  Nocturnal  Heavens. 

THE  SATTELLITKB  OF  JUPITER. — How  Discovered. — Their  Magnitude. — Form  of 
their  Orbits. — Period  of  Revolution. — Eclipses. — Transits. — Occultations. — 
Velocity  of  Light  Discovered. — Terrestrial  Longitude. — Rotation  of  these 
Moons  on  an  Axis . .. 134 


CHAPTER  VIII. 

SATURN,  THE  SEYENTH  PLANET  IN  THE  ORDER  OF  DISTANCE  FROM 
THE  SUN,  SURROUNDED  BY  CONCENTRIC  RINGS,  AND  ATTENDED 
BY  EIGHT  SATELLITES. 

Tho  most  Distant  of  the  Old  Planets.— Its  Light  Faint,  but  Steady.— Synodi- 
cal Revolution. — The  Sidereal  Revolution. — Advances  in  Telescopic  Discov- 
ery.— Galileo  announces  Saturn  to  be  Triple. — Huygens  Discovers  the  Ring. 
— Division  of  the  Ring  into  Two. — Cassini  announces  the  Outer  Ring  the 
Brighter.— Multiple  Division.— Shadow  of  the  Planet  on  the  Ring— Belts 
and  Spots. — Period  of  Rotation  of  the  Planet  and  the  Ring. — Disappearance 
of  the  Ring  Explained.— The  Dusky  Ring. 

SATELLITES  OF  SATUIIN. — By  whom  Discovered. — Eight  in  Number. — Thair 
Distances  and  Periods. — Saturn's  Orbit  the  Boundary  of  the  Planetary  Sys- 
tem, as  known  to  the  Ancients 156 


CONTENTS. 
CHAPTER  IX. 

THE  LAWS  OP  MOTION  AND  GRAVITATION. 

The  Demands  of  Formal  Astronomy.— Those  of  Physical  Astronomy.— Syn- 
opsisot  the  Discoveries  already  made. — Questions  remaining  to  be  Answered. 
— Inquiry  into  Causes. — The  I^tws  of  Motion  demanded. — Rectilineal  Mo- 
tion.—Falling  Bodies.— Law  of  Descent— Motion  of  Projectiles.— Curvilin- 
ear Motion. — First  Law  of  Motion  — Second  Law  of  Motion. — Momentum 
of  Moving  Bodies. — Motion  on  an  inclined  Plane. — The  Centrifugal  Force. 
— Central  Attraction. — Gravitation.—  Laws  of  Motion  applied  to  the  Planets. 
— Questions  Propounded  in  Physical  Astronomy. — Newton'a  Order  of  Inves 
tigution. — His  assumed  Law  of  Gravitation. — Outline  of  his  Demonstration. 
—Its  Importance  and  Consequences. — The  Law  of  Gravitation  embraces  all 
the  Planets  and  their  Satellites.— Gravitation  Resides  in  every  Particle  of 
Matter 166 


.    CHAPTER  X. 

THE  LAWS  OP  MOTION  AND  GRAVITATION   APPLIED  TO  A  SYSTEM    OF 
THREE   REVOLVING  BODIES. 

A  System  of  two  Bodies. — Quantities  Required  in  its  Investigation. — Five  in 
.Number. — Sun  and  Earth. — Sun,  Earth  and  Moon,  as  Systems  of  Three 
Bodies. — The  Sun  supposed  Stationary.— Changed  Figure  «>f  the  Moon's  Or- 
bit.—Sun  Revolving  Changes  the  Position  of  the  Moon's  Orbit.— Solar  Orbit 
Elliptical. — Effects  Resulting  from  the  Inclination  of  the  Moon's  Orbit. — 
Moon's  Motion  above  and  below  the  Plane  of  the  Ecliptic. — Revolution  of 
the  Line  of  Nodes.— Sun,  Earth  and  Planet,  as  the  Three  Bodies.— Perturba- 
tions Destroy  the  Rigor  of  Kepler's  Laws. — Complexity  thus  Introduced. — 
Infinitesimal  Analysis.— Difference  between  Geometrical  and  Analytical 
Reasoning 194 


CHAPTER  XI. 

INSTRUMENTAL  ASTRONOMY. 

Method  for  Obtaining  the  Mass  of  the  Sun.— For  getting  the  Mass  of  a  Planet 
with  a  Satellite. — For  weighing  a  Planet  having  no  Satellite. — For  weighing 
the  Satellites. — Planetary  Distances  to  be  Measured. — Intervals  between 
Primaries  and  their  Satellites  to  be  Obtained.— Intensity  and  Direction  of 
the  Impulsive  Forces  to  be  Determined. — These  Problems  all  Demand  In- 
strumental Measures. — Differential  Places. — Absolute  Places. — The  Transit 
Instrument — Adjustments. — Instrumental  Errors. — Corrections  Due  to  Va- 
rious Causes-^American  Method  of  Transits.— Meridian  Circle.— The  De- 
clinometer  210 


CHAPTER  XII. 

URANUS,   THE  EIGHTH  PLANET  IN  THE  ORDER  OP  DISTANCE  FROM 
THE  SUN.       . 

Accidentally  Discovered  by  Sir  William  Herschell. — Announced  as  a  Comet. 
—Its  Orbit  proved  it  to  be  a  Superior  Planet.— The  Elements  of  its  Orbit 
Obtained.— Arc  of  Retrogradation.— Period  of  Revolution.— Figure  of  the 
Planet— Inclination  of  its  Orbit.— Six  Satellites  Announced  by  the  Elder 
Herschell. — Four  of  these  now  Recognized. — Their  Orbital  Planes  and  Di- 
rections of  Revolution  Anomalous. — Efforts  made  to  Tabulate  the  Places  of 
Uranus  Unsuccessful.— This  Leads  to  the  Discovery  of  a  New  Exterior 
Planet §44 


CONTENTS. 


CHAPTER  XIII. 

NEPTUNE,   THE  NINTH  AND  LAST  KNOWN  PLANET  IN  THE  ORDEE  OF 
DISTANCE  FROM  THE  SUN. 

PAG* 

Jranns  Discovered  by  Accident.— Ceres  by  Eesearch  with  the  Telescope.— 
Rediscovered  by  Mathematical  Computation.— The  Perturbations  of  Uranus. 
—Not  due  to  any  known  Cause.— Assumed  to  Arise  from  an  Exterior  Planet. 
— Nature  of  the  Examination  to  find  the  Unknown  Planet.— Undertaken  at 
the  same  time  by  two  Computers. — Computation  Assigns  a  Place  to  the  Un- 
known Planet.— Discovered  by  the  Telescope.— Discoveries  Resulting.— A 
Satellite  Detected.— The  Mass  of  Neptune  thus  Determined.— Neptune  s 
Orbit  the  Circumscribing  Boundary  of  the  Planetary  System 269 


CHAPTER  XIY. 

THE  COMETS. 

Objevis  of  Dread  in  the  Early  Ages.— Comets  Obey  the  Law  of  Gravitation 
and  Revolve  in  some  one  of  the  Conic  Sections. — Characteristics  of  these 
Curves.— Comet  of  1680  Studied  by  Newton.— Comet  of  1682  named  "  Hal- 
ley's  Comet"— Its  History.— Its  Return  Predicted.— Perihelion  Passage 
Computed.— Passes  its  Perihelion  18th  April,  1759  —Elements  of  its  Orbit. 
— Physical  Constitution. — Nucleus. — Envelopes. — Tail. — Intense  Heat  Suf- 
fered* by  some  Comets  in  Perihelio.— Dissipation  of  the  Coinetic  Matter. — 
Encke's  Comet— A  Resisting  Medium.— Deductions  from  Observation.— 
Biela's  Couiet— Divided.— N  umber  of  Comets. 


CHAPTER  XT. 

THE  SrjN  AND  PLANETS  AS  PONDERABLE  BODIES. 

General  Circumstances  of  the  System. — The  Sun. — His  Diameter  and  Mass. — 
Gravity  at  the  Surface.— Mercury.— His  Mass  and  Perturbations.— Venus  as 
a  Ponderable  Body.— Long  Equation  of  Venus  and  the  Earth.— The  Earth 
and  Moon  as  Heavy  Bodies.— Figure  and  Mass  of  the  Earth. — Precession — 
Aberration.— Nutation.— Mars.— His  Mass  and  Density. — Gravity  at  His  Sur- 
face.— The  Asteroids. — Jupiter's  System. — Saturn. — 11  is  Moons  and  Rings  as 
Ponderable  Bodies.— Uranus.— Neptune.— Stability  of  the  whole  System... .  303 


CHAPTER  XVI. 

THE  NEBULAR  HYPOTHESIS. 

The  Arrangement  of  the  Solar  System. — The  Phenomena  for  which  Gravitation 
is  Responsiule^— The  Phenomena  Remaining  to  be  Accounted  for. — Nebu- 
lous Matter  as  found  in  Comets. — Nebulous  Matter  Possibly  in  the  Heavens. 
— The  Entire  Solar  System  once  a  Globe  of  Nebulous  Matter. — Motion  of 
Rotation. — Radiation  of  Heat. — Condensation  and  its  Effects Rings  disen- 
gaged from  the  Equator  of  the  Revolving  Mass. — Formation  of  Planets  and 
of  Satellites 8U 


INTRODUCTION 


THE  great  dome  of  the  heavens,  filled  with  a  countless 
multitude  of  stars,  is  beyond  a  doubt  the  most  amazing 
spectacle  revealed  by  the  sense  of  sight.  It  has  excited 
the  admiration  and  curiosity  of  mankind  in  all  ages  of 
the  world.  The  study  of  the  stars  is  therefore  coeval 
with  our  race,  and  hence  we  find  many  discoveries  in  the 
heavens  of  whose  origin  neither  history  nor  tradition  can 
give  any  account.  The  science  of  Astronomy,  embracing, 
as  it  does,  all  the  phenomena  of  the  celestial  orbs,  has 
furnished  in  all  ages  the  grandest  problems  for  the  exer- 
cise of  human  genius.  In  the  primitive  ages  its  ad- 
vances were  slow,  but  by  patient  watching,  and  by  dili- 
gent and  faithful  records  transmitted  to  posterity  from 
generation  to  generation,  the  mysteries  which  fill  the 
heavens  were  one  by  one  mastered,  until  at  length,  in 
our  own  age,  there  remains  no  phenomenon  of  motion 
unexplained,  while  the  distances,  magnitudes,  masses, 
reciprocal  influences,  and  physical  constitution  of  the 
celestial  orbs  have  been  approximately  revealed.  In  a 
former  volume  an  attempt  was  made  to  trace  the  career 
of  discovery  among  the  stars,  and  to  exhibit  the  successive 
steps  by  which  the  genius  of  man  finally  reached  the  so- 
lution of  the  great  problem  of  the  universe. 

The  performance  of  that  task  did  not  permit  the  special 
study  of  any  one  object,  except  so  far  as  it  was  required 
in  the  march  of  the  general  investigation.  It  is  our 


X  INTRODUCTION. 

object  DOW  to  execute  what  was  then  promised,  and  to 
examine  in  detail  the  various  bodies  which  are  allied  to 
the  sun,  constituting  (as  we  shall  find)  a  delicately  or- 
ganized system  of  revolving  worlds,  a  complex  mechanical 
structure,  whose  stability  has  challenged  the  admiration 
of  all  thinking  minds,  and  whose  organization  has  fur- 
nished the  most  profound  themes  of  human  investiga- 
tion. 

The  plan  adopted  will  lead  us  to  present  clearly  all  the 
facts  and  phenomena  resulting  from  observation;  with 
these  facts  the  student  may  exercise  his  own  genius  in 
attempting  to  account  for  the  phenomena,  before  proceed- 
ing to  accept  the  explanation  laid  down  in  the  text. 

To  aid  the  memory  and  to  present  a  systematic  investi- 
gation, we  shall  adopt  the  simple  order  of  distance  from 
the  solar  orb,  commencing  with  that  grand  central  lumi- 
nary, and  proceeding  outward  from  planet  to  planet, 
until  we  shall  develop  all  the  phenomena  employed  in  the 
discovery  of  the  great  law  of  universal  gravitation.  With 
a  knowledge  of  this  law  the  worlds  already  examined 
cease  to  be  isolated,*  and  arrange  themselves  under  the 
empire  of  gravitation  into  a  complex  system,  the  delicate 
relations  of  whose  parts,  leads  to  new  discovery  and  to 
the  final  perfection  of  the  system  of  solar  satellites. 

Having  closed  our  investigation  of  the  planets  and  their 
tributary  worlds,  we  shall  render  an  account  of  those 
anomalous  bodies  called  comets,  which,  by  the  sudden- 
ness of  their  appearance,  their  rapid  and  eccentric  mo- 
tions, and  the  brilliant  trains  of  light  which  sometimes 
attend  them,  have  excited  universal  interest,  not  unat- 
tended with  alarm  in  all  ages  of  the  world. 

Before  passing  to  the  execution  of  this  plan,  we  must 
examine,  to  some  extent,  the  phenomena  of  the  nocturnal 


INTRODUCTION.  XI 

heavens,  as  the  stars  furnish  the  fixed  points  to  which 
all  moving  bodies  are  referred. 

To  the  eye  the  heavens  rise  as  a  mighty  dome,  a  vast 
hollow  hemisphere,  on  whose  internal  surface  the  glitter- 
ing stars  remain  forever  fixed.  In  case  we  watch  through 
an  entire  night,  we  find  the  groupings  of  stars  slowly 
rising  from  the  east,  gradually  reaching  their  culmina^ 
tion,  and  then  gently  sinking  in  the  west.  A  more  at- 
tentive examination  enables  the  eye  to  detect  some  of 
these  groups  of  stars  toward  the  north  which  ever  remain 
visible,  rising,  culminating,  and  descending,  but  never 
sinking  below  the  horizon.  Every  star  in  this  diurnal 
revolution,  as  it  is  called,  is  found  to  describe  a  circle, 
precisely  as  if  the  concave  heavens  were  a  hollow  sphere 
to  which  the  stars  were  attached,  and  that  this  hollow 
globe  were  made  to  revolve  about  a  fixed  axis,  passing 
through  its  center.  Indeed,  we  find  by  attentively  watch- 
ing, that  this  hypothesis  of  a  spherical  heavens  accounts 
for  all  the  phenomena  already  presented.  As  the  stars  are 
situated  nearer  to  the  extremity  of  the  axis  of  revolution 
the  circles  they  describe  grow  smaller  and  smaller,  until, 
finally,  we  find  one  star  which  remains  fixed,  and  this  one 
must  be  at  the  point  where  the  axis  of  the  heavens 
pierces  the  celestial  sphere.  This  is  called  the  north 
star  ;  and  the  point  in  which  the  axis  pierces  the  heavens 
is  called  the  north  pole.  The  opposite  point  is  called 
the  south  pole. 

Only  one  half  of  the  celestial  sphere  is  visible  at  one 
time  above  the  horizon,  but  this  spherical  surface  ex- 
tends beneath  the  horizon,  and  forms  a  complete  sphere, 
encompassing  us  on  all  sides,  while  its  center  seems  to  be 
occupied  by  the  earth.  It  is  true  that,  in  the  day-time, 
the  stars  fade  from  the  sight  in  the  solar  blaze,  but  they 


Xll  INTRODUCTION. 

are  not  lost ;  they  still  fill  the  heavens,  as  we  shall  see 
hereafter,  and  the  starry  sphere  sweeps  unbroken  entirely 
round  the  earth. 

These  great  truths,  the  diurnal  revolution  of  the  heav- 
ens, its  spherical  form,  the  central  position  of  the  earth, 
the  north  polar  star,  the  axis  of  the  heavens,  the  circles 
described  by  the  stars,  were  among  the  discoveries  of 
primitive  antiquity,  and  are  matters  of  the  most  simple 
observation. 

The  spherical  form  of  the  heavens  was  soon  imitated, 
and  the  artificial  globe  became  one  of  the  first  astronom- 
ical instruments.  On  this  artificial  globe  certain  lines 
were  drawn  to  imitate  those  described  in  the  heavens  by 
the  celestial  orbs,  and  as  these  lines  must  henceforth 
form  a  part  of  our  language  we  proceed  to  give  the  fol- 
lowing Definitions : — 

A  great  circle  is  one  whose  plane  passes  through  the 
center  of  the  sphere. 

A  small  circle  is  one  whose  plane  does  not  pass  through 
the  center  of  the  sphere. 

The  axis  of  the  heavens  is  an  imaginary  line  passing 
through  the  center  of  the  earth,  and  about  which  the 
heavens  appear  to  revolve  once  in  twenty-four  hours. 

A  meridian  is  a  great  circle  passing  through  the 
highest  point  of  the  celestial  sphere  (called  the  zenith) 
and  the  axis  of  the  heavens. 

The  equator  or  equinoctial  is  a  great  circle,  perpen- 
dicular to  the  axis  of  the  heavens,  and  half-way  between 
the  north  and  south  polar  points. 

These  important  lines  have  been  employed  from  the 
earliest  ages  in  the  study  of  the  heavenly  bodies,  and 
having  thoroughly  mastered  their  meaning  and  position 
we  are  prepared  to  examine  any  changes  of  location  which 


INTRODUCTION.  X1U 

may  be  discovered  among  the  vast  multitude  of  shining 
bodies  which  go  to  fill  up  the  concave  of  the  celestial 
sphere. 

We  shall  proceed,  then,  without  further  delay,  to  the 
execution  of  the  plan  already  laid  down. 


CHAPTER  I. 

THE  SUN,  THE  CENTRAL  ORB  OF  THE  PLANETARY 
SYSTEM. 

DISCOVERIES  OP  THE  ANCIENTS.— THE  SOURCE  OF  LIFE  AND  LIGHT  AKB 
HEAT.— THR  SUN'S  MOTION  AMONG  THE  STARS.— Hw  OBBIT  CIBCULAB.— 
LENGTH  OF  THE  YEAE.— INEQUALITY  OF  THE  SUN'S  MOTION.— EXPLAINED 

BY  HlPPARCHUS.— SOLAB     ECLIPSES.— THEIR  FlRST  PREDICTION. 

DISCOVERIES  OF  THE  MODERNS.— THE  SUN'S  DISTANCE.— His  HORIZONTAL 
PARALLAX.— IMPORTANCE  OF  THIS  ELEMENT.— MEABUBED  BY  THE  TBANSIT  or 
VENUS.— THE  SUN'S  ACTUAL  DIAMETER  AND  SEAL  MAGNITUDE.— His  ROTA- 
TION.— THE  SOLAS  SPOTS. — THEIR  PERIODICITY. — SPECULATIONS  AS  TO  THB 
PHYSICAL  CONSTITUTION  OF  THE  SUN. 

THE  sun  is  beyond  comparison  the  grandest  of  all  the 
celestial  orbs,  of  "which  we  have  any  positive  knowledge. 
The  inexhaustible  source  of  the  heat  which  warms  and 
vivifies  the  earth,  and  the  origin  of  a  perpetual  flood  of 
light,  which,  flying  with  incredible  velocity  in  all  direc- 
tions, illumines  the  planets  and  their  satellites,  lights  up 
the  eccentric  comets,  and  penetrates  even  to  the  region 
of  the  fixed  stars ;  it  is  not  surprising  that  in  the  early 
ages  of  the  world,  this  mighty  orb  should  have  been  re- 
garded as  the  visible  emblem  of  the  Omnipotent,  and  as 
such  should  have  received  divine  honors. 

On  the  approach  of  the  sun  to  the  horizon  in  the  early 
dawn,  his  coming  is  announced  by  the  gray  eastern  twi- 
light, before  whose  gradual  increase  the  brightest  stars 
and  even  the  planets  fade  and  disappear.  The  coming 
splendor  grows  and  expands,  rising  higher  and  yet  higher, 
until,  as  the  first  beam  of  sunlight  darts  on  the  world,  not 
a  star  or  planet  remains  visible  in  the  whole  heavens,  and 


16  T  H  E     S  U  N . 

even  the  moon,  under  this  flood  of  sunlight,  shines  only 
as  a  faint  silver  cloud. 

This  magnificent  spectacle  of  the  sunrise,  together 
with  the  equally  imposing  scenes  which  sometimes  ac- 
company the  setting  sun,  must  have  excited  the  curiosity 
of  the  very  first  inhabitants  of  the  earth.  This  curiosity 
led  to  a  more  careful  examination  of  the  phenomena  at- 
tending the  rising  and  setting  sun,  when  it  was  discovered 
that  the  point  at  which  this  great  orb  made  his  appear- 
ance was  not  jfcree?,  but  was  slowly  shifting  on  the  horizon, 
the  change  being  easily  detected  by  the  observation  of  a 
few  days.  Hence  was  discovered,  in  the  primitive  ages — 

THE  SUN'S  APPARENT  MOTION. — In  case  the  sun  is 
observed  attentively  from  month  to  month  it  will  be  found 
that  the  point  of  sunrise  on  the  horizon  moves  slowly,  for 
a  certain  length  of  time,  toward  the  south.  While  this 
motion  continues,  the  sun,  at  noon,  when  culminating  on 
the  meridian,  reaches  each  day  a  point  less  elevated  above 
the  horizon,  and  the  diurnal  arc  or  daily  path  described 
by  the  sun  grows  shorter  and  shorter.  At  length  a 
limit  is  reached ;  the  point  of  sunrise  ceases  to  advance 
toward  the  south,  remaining  stationary  a  day  or  two, 
and  then  slowly  commences  its  return  toward  the  north. 
This  northern  movement  continues ;  each  day  the  sun 
mounts  higher  at  his  meridian  passage,  the  diurnal  aro 
above  the  horizon  grows  longer  and  longer,  until,  again, 
a  northern  limit  is  reached,  beyond  which  the  sun  never 
passes.  Here  he  becomes  stationary  for  one  or  two  days, 
and  then  commences  his  return  toward  the  south.  Thus 
does  the  sun  appear  to  vibrate  backward  and  forward  be- 
tween his  southern  and  northern  limits,  marking  to  man 
a  period  of  the  highest  interest,  for  within  its  limits  the 
spring,  the  summer,  the  autumn,  and  the  winter,  have 


THE    SUN.  17 

run  their  cycles,  and  by  their  union  have  wrought  out 
the  changes  of  the  year. 

The  length  of  this  important  period  was,  doubtless, 
first  determined  by  counting  the  days  which  elapsed  from 
the  time  when  the  sun  rose  behind  some  well-defined 
natural  object  in  the  horizon  until  his  return  in  the  same 
direction  to  the  same  point  of  rising:  Of  course,  these 
changes  in  the  sun's  place  were  studied  with  profound 
attention.  They  were  among  the  first  celestial  phenom- 
ena discovered,  and  among  the  first  demanding  explana- 
tion. The  stars  were  found  never  to  change  their  points 
of  rising,  culmination,  and  setting.  Their  diurnal  arc 
remained  forever  the  same,  and  the  amount  of  time  they 
remained  above  the  horizon  depended  on  their  distance 
from  the  north  polar  point. 

Observation  having  thus  revealed  the  fact  that  the  sun 
was  undoubtedly  moving  alternately  north  and  south,  a 
more  critical  research  showed  the  equally  important 
truth,  that  this  great  luminary  was  slowly  shifting  its 
place  among  the  fixed  stars.  This  was  not  so  readily 
determined ;  but  by  noting  the  brilliant  stars  which  first 
appeared  in  the  evening  twilight,  after  sunset,  it  was 
soon  discovered  that  these  stars  did  not  long  remain  vis- 
ible. Indeed,  the  whole  starry  heavens  seemed,  from 
night  to  night,  to  be  plunging  downward  to  overtake  the 
setting  sun,  or  rather,  that  the  sun  himself  was  mounting 
upward  to  meet  the  stars,  and  thus  was  discovered  a  solar 
motion  in  a  direction  opposed  to  the  diurnal  revolution 
of  the  heavens. 

From  month  to  month  the  sun  was  seen  to  advance 
among  the  stars,  and  at  the  end  of  an  entire  year,  after 
all  the  former  changes  of  northern  and  southern  motion 
had  been  accomplished,  the  sun  was  found  to  return  to 


18  THE     SUN. 

the  same  group  of  fixed  stars  from  whence  he  set  out ; 
and  thus  it  became  manifest  that  this  revolution  among 
the  stars  was  identical  in  period  with  the  changes  from 
north  to  south,  and  hence  these  phenomena  had,  in  all 
probability,  a  common  origin. 

Here  was  the  first  great  problem  offered  for  solution 
to  the  old  astronomers.  The  facts  and  phenomena  were 
carefully  studied,  and  the  reader  may  now  exercise  his 
own  power  of  thought  in  an  effort  to  explain  the  facts 
recorded,  before  accepting  the  solution  we  are  about  to 
present. 

An  examination  of  the  points  of  rising,  of  culmination, 
and  of  setting,  of  the  fixed  stars,  showed  them  to  be  ab- 
solutely invariable,  and  in  case  these  glittering  points 
could  leave  behind  them,  in  their  diurnal  revolution, 
lines  of  silver  light,  sweeping  upward  from  their  point  of 
rising  to  the  meridian,  and  downward  to  the  point  of 
setting,  these  lines  of  light  would  be  seen  to  be  parallel 
circles.  All  the  stars  north  of  the  equinoctial  (in  the 
region  of  the  earth  w&  inhabit)  describe  diurnal  circles, 
of  which  more  than  one  half  is  above  the  horizon,  while 
all  the  stars  south  of  the  same  line  sweep  round  in  circles, 
of  which  less  than  half  lies  above  the  same  plane.  Any 
star,  precisely  on  the  equinoctial,  half  way  between  the 
north  and  south  poles,  passes  one  half  its  revolutio^ 
above  and  the  other  half  below  the  horizon. 

These  facts  being  carefully  noted,  it  was  seen  that  in 
case  the  sun,  on  any  day  of  its  annual  journey,  chanced 
to  coincide  with  a  fixed  star,  that  for  that  day  the  sun 
and  star  would  describe  the  same  diurnal  circle,  and 
would  remain  above  the  horizon  an  equal  length  of  time. 
Thus  along  the  sun's  path  it  became  possible  to  select  a 
number  of  stars  over  which  the  sun  passed,  and  which 


THE     SUN.  >D 

•would  by  their  position  mark  his  route  -in  the  havens. 
To  aid  in  this  investigation,  as  well  as  for  some  other 
purposes,  the  ancients  erected  a  vertical  staff  on  a  level 
plane,  and  then  noted  where  the  shadow  of  the  top  of  the 
staff  fell  at  noon  each  daj  throughout  the  year.  This 
instrument  was  called  a  gnomon,  and  its  use  revealed 
many  important  facts  in  the  solar  motion,  and  detected 
others  hitherto  overlooked.  If  on  the  same  day  we  note 
carefully  the  length  of  the  shadow  of  the  gnomon  a  little 
while  before  and  after  noon,  we  shall  find  the  shadow 
slowly  decrease  in  length  as  the  sun  rises  to  its  culmina- 
tion; and  immediately  after  passing  the  meridian  the 
shadow  commences  to  increase  in  length.  Mark  the  point 
where  the  shortest  shadow  fell,  and  the  line  joining  this 
point  with  the  foot  of  the  gnomon  is  a  north  and  south 
line,  and  on  this  line  all  the  noon  shadows  will  fall 
throughout  the  entire  year. 

By  a  careful  examination  it  was  discovered  that  the 
noon  shadow  on  the  day  of  the  winter  solstice  or  southern 
limit  always  fell  on  the  same  point.  The  same  was  true  of 
the  noon  shadow  on  the  day  of  the  summer  solstice  or 
northern  limit.  These  points  were  exactly  opposite  each 
other  on  the  sun's  apparent  orbit  (or  path  among  the 
stars).  It  was  further  discovered,  that  selecting  any  day 
iji  the  year,  the  noon  shadow  for  that  day  invariably  fell 
on  the  same  point  as  it  had  done  on  preceding  years ;  and 
hence  it  became  manifest  that  thd  sun's  track  among  the 
stars  did  not  change  from  year  to  y^ar. 

The  question  now  arose  as  to  the  figure  of  the  sun's 
path  :  was  that  figure  a  circle  ?  and  did  the  sun  move 
with  uniform  velocity  ?  As  all  the  stars  described  diur- 
nal circles ;  as  this  curve  was  the  simplest  as  well  as  the 
most  beautiful  of  curves ;  as  its  curvature  was  every  where 


20 


THE      SUN. 


the  same ;  as  it  had  neither  beginning  nor  ending,  it  was 
early  adopted  as  the  celestial  curve,  shadowing  forth, 
even  in  its  form,  the  ceaseless  journeys  of  the  revolving 
worlds.  It  was  assumed  then  that  the  sun  swept  round 
the  sphere  of  the  heavens  once  a  year,  with  uniform 
velocity,  in  a  circular  orbit,  of  which  the  earth  was  in  the 
center. 

This  hypothesis  accounted  fully  for  all  the  discovered 
phenomena,  and  justly  ranks  among  the  most  important 
of  the  primitive  discoveries. 

The  gnomon  gave  to  the  old  astronomers  a  ready 
means  not  only  of  tracing  the  sun's  path  among  the  stars, 
but  also  of  measuring  the  inclination  of  the  plane  of  the 
ecliptic  to  the  plane  of  the  equinoctial.  This  is  readily 
seen  from  the  subjoined  figure. 


Let  AB  represent  the  gnomon,  \f  the  shadow  of  the 
vertex  at  noon  on  the  day  of  the  summer*  solstice,  and 
A"  the  shadow  at  noon  on  the  day  of  the  winter  solstice. 
Then  will  the  angle  A7  A  A"  measure  the  entire  motion 
of  the  sun  from  north  to  south ;  and  as  one  half  of  this 
motion  lies  north  and  the  other  half  south  of  the  equinoo 


THE      SUN.  •  21 

tial,  it  follows  that  half  the  angle,  A' A  A,"  measures  the 
inclination  of  the  ecliptic  to  the  equinoctial. 

In  the  earliest  ages  it  was  assumed  that  the  sun's  orbit 
was  absolutely  fixed  among  the  stars,  and  that  the  points 
in  which  this  circle  crossed  the  equinoctial  were  in  like 
manner  invariable.  These  points  .of  intersection  are  of 
the  highest  importance.  That  one  through  which  the 
sun  passes  in  going  from  south  to  north,  is  called  the 
Vernal  Equinox,  while  the  opposite  point,  through  which 
the  solar  orb  passes  in  going  from  north  to  south,  is 
called  the  Autumnal  Equinox.  On  the  day  of  the 
equinoxes,  as  the  sun's  center  was  then  on  the  equinoc- 
tial, the  diurnal  arc  described  by  the  sun  would  lie  one 
half  above,  a#d  the  other  half  below  the  horizon,  making 
the  length  of  day  and  night  precisely  equal. 
~  Among  tie  ancient  nations  the  day  of  the  vernal  equi- 
nox was  an  object  of  especial  interest,  as  it  heralded  the 
coming  of  spring,  and  its  approach  was  marked  by  the 
rising  of  a  certain  bright  star  in  the  early  dawn  of  the 
morning.  Now,  in  case  the  vernal  and  autumnal  equi- 
noxes were  invariable,  the  same  star  by  its  heliacal 
rising,  (as  it  was  called,)  would  mark  the  crossing  of  the 
equinoctial  by  the  sun  in  the  spring  and  the  equality  of 
day  and  night.  After  the  lapse  of  few  centuries  it  was 
discovered,  by  the  length  of  the  noon  shadow  of  the  gno- 
mon, that  the  sun  had  reached  the  equinoctial  point,  and 
yet  the  sentinel  star  did  not  make  its  appearance.  Either 
the  equinox  or  the  star  was  in  motion.  It  was  soon 
decided  that  the  vernal  and  autumnal  equinoxes  are  both 
slowly  moving  backwards  along  the  equinoctial,  and  thus 
the  sun  crosses  this  celestial  circle  each  year  a  little  be- 
hind the  point  of  the  preceding  year. 

The  ancient  nations  all  seem  to  have  attained  to  a 


22  THE     SUN. 

knowledge  of  this  great  truth,  and  some  of  them  are  said 
to  have  fixed  the  period  in  which  the  vernal  equinox 
retrogrades  around  the  entire  heavens,  a  period  of  nearly 
twenty-six  thousand  years ;  as  this  is  a  matter  of  simple 
observation,  and  as  the  rate  of  motion  can  be  obtained  by 
comparing  recorded  observations,  made  at  intervals  of 
four  hundred  or  five  hundred  years,  we  may  readily  cre- 
dit the  statement  that  this  period  became  known  even 
anterior  to  the  commencement  of  authentic  history. 

This  discovery  of  the  retrocession  of  the  equinoxes  led 
to  a  more  critical  examination  of  the  sun's  apparent  mo- 
tion. This  motion  had  been  assumed  to  be  uniform,  and 
in  case  this  hypothesis  could  be  maintained,  the  solar  orb 
ought  to  occupy  an  equal  amount  of  time  in  passing  over 
the  two  portions  of  its  orbit  north  and  south  of  the  equi- 
noctial, that  is,  the  number  of  days  from  the  vernal  to 
the  autumnal  equinox  ought  to  be  precisely  equal  to 
the  number  of  days  from  the  autumnal  to  the  vernal 
equinox. 

The  Greek  astronomer  Hipparchus  was  the  first  to  dis- 
cover the  important  truth  that  an  inequality  existed  in 
these  two  periods.  He  found  from  his  own  observations 
that  the  sun  occupied  eight  days  more  in  tracing  the 
northern  than  it  did  in  traversing  the  southern  portion 
of  its  orbit.  This  was  a  discovery  of  the  highest  import- 
ance, as  it  seemed  to  involve  the  then  incredible  fact,  that 
the  lord  of  the  celestial  sphere,  the  great  source  of  life, 
and  light,  and  heat,  traveled  among  the  stars  with  a  vari- 
able velocity. 

In  case  the  solar  orbit  was  indeed  a  circle,  this  in- 
equality of  motion  seemed  to  be  impossible.  The  circular 
figure  of  the  orbit  could  not  be  abandoned,  neither  was  it 
possible  on  philosophical  principles  to  give  up  the  hypo- 


T  H  E     S  U  N  ,  23 

thesis  of  uniform  motion.  Here  then  was  presented  a 
problem  of  the  deepest  interest,  to  preserve  the  circular 
figure  of  the  solar  orbit  and  the  uniform  motion  of  the 
sun,  and  at  the  same  time  render*  a  satisfactory  account 
of  the  inequality  discovered  in  the  periods  during  which 
the  sun  remained  north  and  south  of  the  equinoctial. 
This  problem  was  solved  by  Hipparchus;  and  before  pro- 
ceeding to  examine  the  reasoning  of  the  old  Greek,  let 
the  student  exercise  his  own  genius  in  an  attempt  to  ex- 
plain the  ascertained  facts. 

Hitherto  it  had  been  assumed,  not  only  that  the  sun's 
orbit  was  circular,  and  that  his  motion  was  uniform,  but 
also  that  the  earth  occupied  the  exact  center  of  the  circle 
in  which  the  sun  traveled  round  the  heavens.  By  pro- 
found study  Hipparchus  discovered  that  all  the  facts 
could  be  explained  by  giving  to  the  earth  a  position  not 
in  the  center  of  the  sun's  orbit,  but  somewhat  nearer  to 
that  portion  of  the  solar  orbit  where  his  motion  was 
most  rapid.  This  will  become  evident  from  the  figure. 
Let  the  circle  A  B  C  D  represent  the  sun's  circular 
orbit,  in  which  the  sun  is  supposed  to  move  uniformly. 
This  motion  will  only  appear  uniform  to  a  spectator  at 
the  center  0.  If  the  observer  be  removed  to  0',  and 
the  line  E  E'  be  drawn  perpendicular  to  0  0',  the  por- 
tion E'  A  B  E  of  the  orbit  will  require  a  longer  time 
for  its  description  than  the  portion  E  C  D  E',  and  hence 
in  the  former  the  sun  will  appear  to  move  slower  than 
in  the  latter.  Indeed,  it  is  manifest  that  the  point  V, 
on  the  line  0  (X  prolonged,  is  the  place  of  swiftest 
motion,  while  the  opposite  point  V  is  that  in  which 
the  sun  will  appear  to  move  slowest. 


24 


THE     SUN. 


Hipparchus,  not  satisfied  with  thus  rendering  a  general 
explanation  of  the  phenomenon,  undertook  to  determine 
the  actual  place  of  the  earth  inside  the  solar  orbit,  or 
the  value  of  the  distanoe  00',  which  is  called  the  eccen- 
tricity. Here  is  another  problem  for  the  examination  of 
the  student.  It  may  be  solved  by  simply  knowing  how 


many  days  longer  the  sun  remained  north  of  the  equi- 
noctial than  it  did  on  the  south  of  this  circle.  This 
quantity  we  have  already  given.  By  dividing  the  circle 
A  B  C  D  into  as  many  equal  parts  as  there  are  days  in 
the  year,  and  by  drawing  F  F'  through  the  center  0, 
and  perpendicular  to  V  V7,'  we  have  only  to  lay  off  from 
F  to  E  half  the  excess  in  days,  and  draw  E  E'  parallel 
to  F  F',  and  it  will  give  at  0'  the  true  place  of  the  earth, 
and  0  0'  will  be  the  eccentricity.  An  observer  at  0' 
will  see  all  phenomena  actually  detected  in  the  sun's 
motion,  while  the  circular  orbit  and  uniform  velocity  are 
rigorously  retained. 

Having  determined  the  earth's  eccentricity,  it  was  now 


T  H  E     B  U  N  .  25 

very  easy  to  calculate  the  sun's  place  from  day  to  day 
during  his  entire  revolution  among  the  fixed  stars.  This 
was  actually  done  by  the  old  astronomers ;  and  as  the 
computed  places  agreed  with  those  observed  within  the 
limits  of  observation,  with  the  rude  instruments  then  in 
use,  no  further  advance  would  be  made  in  the  solar  "mo- 
tions. 

^ECLIPSES  OF  THE  SUN. — No  one  has  ever  beheld  the 
total  disappearance  of  the  sun  in  the  day-time  without  a 
feeling  of  awe  creeping  through  his  frame,  and,  even  now, 
when  modern  science  predicts  the  coming  of  these  amazing 
phenomena  with  unerrir<£  precision,  a  total  eclipse  of  the 
sun  never  fails  to  inspire  a  certain  feeling  of  gloomy  ap- 
prehension. What,  then,  must  have  been  the  effect  in 
the  rude  ages  of  the  world  of  the  fading  out  of  the  sun  in 
mid-course  through  the  heavens?  Human  genius,  of 
course,  bent  all  its  energies  to  the  resolution  of  the  great 
problems  involved  in  the  occurrence  of  an  eclipse  of  the 
sun.  The  first  effort  was  directed  to  the  discovery  of  the 
cause  of  these  startling  phenomena ;  and,  this  once  de- 
termined, the  second  great  effort  was  put  forth  to  so 
master  all  the  circumstaiKjes  as  not  only  to  explain  the 
eclipse  but  to  predict  its  ^vming. 

CAUSE  OF  A  SOLAR  ECLIPSE. — In  searching  for  the 
jause  by  which  the  sun  might  be  hidden,  it  was  at  once 
evident  that  there  was  but  one  object  in  the  heavens  suf- 
ficiently large  to  hide  the  whole  surface  of  the  sun.  This 
body  was  the  moon.  Thus  attention  was  directed  to  the 
lunar  orb,  and  it  was  soon  noticed  that,  while  the  bright 
stars  and  planets  became"  visible  in  the  darkness  attending 
an  eclipse  of  the  sun,  yet  the  brightest  object  in  the  heavens 
after  the  sun,  was  never  visible  during  an1  eclipse.  The 
moon  was  found  to  move  among  the  stars  with  a  velocity 

2 


26  T  H  E     S  U  N  . 

far  greater  than  that  of  the  sun.  It  was,  moreover,  seen 
that  the  moon's  path  crossed  that  of  the  sun  twice  during 
every  revolution  of  the  moon,  and  examining  still  more 
closely,  it  was  discovered  that  no  eclipse  of  the  sun  ever 
occurred  except  at  the  new  moon.  Now  this  rapidly 
revolving  globe  was  evidently  the  nearest  to  the  earth  of 
all  the  heavenly  bodies.  It  was  seen,  when  a  silver 
crescent,  sometimes  to  pass  over  and  hide  the  larger  stars 
which  fell  in  its  path  ;  it  was  also  found  that  the  moon, 
though  invisible  during  a  solar  eclipse,  always  appeared 
immediately  after  very  near  the  sun  and  as  a  slendei 
crescent  of  light.  These  facts  all  combined  to  provfr 
beyond  a  question  that  the  sun  was  eclipsed  by  being 
covered  by  the  dark  body  of  the  moon.  The  cause  of 
the  eclipse  was.  thus  reached,  and  it  now  remained  to  rob 
the  phenomenon  of  its  terrors  by  predicting  when  it  might 
be  expected. 

To  predict  a  solar  eclipse  with  precision  is  a  problem 
of  great  difficulty,  even  with  the  present  extended  knowl- 
edge of  the  laws  and  structure  of  the  solar  system.  And 
yet  we  are  informed  that  the  old  Greek  astronomers  suc- 
ceeded in  the  resolution  of  this  complex  problem.  This 
may  have  been  done  by  long  and  persevering  care  in  the 
record  of  these  phenomena ;  for  in  case  all  the  eclipses 
visible  at  any  given  place  are  recorded  year  after  year 
for  a  period  of  nineteen  years,  it  will  be  found  that  for 
the  next  period  of  nineteen  years  eclipses  will  happen  on 
the  same  days  and  in  the  same  order ;  so  that  an  astron- 
omer, whose  diligence  had  been  rewarded  by  the  discovery 
of  this  grand  truth,  might  acquire  the  highest  renown 
among  his  countrymen  and  throughout  the  world  by  his 
suDerior  wisdom  in  predicting  the  coming  of  an  eclipse, 


T  H  E     S  U  N  .  27 

though  no  special  genius  was  put  forth  in  the  resolution 
of  this  great  problem. 

We  are  not  quite  certain,  however,  that  the  prediction 
of  the  first  announced  solar  eclipse  may  not  have  been 
accomplished  by  the  application  of  powerful  thought  and 
persevering  observation.  In  case  the  effort  were  now 
made  to  predict  a  solar  eclipse ;  as  a  starting  point  'we 
know  that  no  eclipse  of  the  sun  ever  occurred  except  at 
the  new  moon.  But  at  the  time  of  a  total  eclipse  of  the 
sun  the  moon  is  interposed  precisely  between  ttie  eye  of 
the  observer  and  the  sun,  and  a  line  joining  the  centers 
of  these  two  great  luminaries,  produced  to  the  earth, 
passes  through  the  place  of  the  observer.  Hence,  on  the 
day  and  at  the  hour  of  an  eclipse  the  new  moon  must  be 
in  the  act  of  passing  from  one  side  of  the  sun's  path  to 
the  other.  To  render  an  eclipse  possible  two  conditions 
must  be  fulfilled  at  the  same  time ;  the  moon  must  be 
neiVj  and  the  moon's  center  must  be  in  the  act  of  cross- 
ing the  sun's  orbit.  If  the  sun's  annual  route  in  the 
heavens  were  marked  among  the  stars  by  a  line  of  golden 
light,  and  the  moon's  motion  be  attentively  watched,  it 
will  be  found  that  at  every  one  of  her  revolutions  she 
crosses  this  golden  line  twice.  The  point  of  her  crossing 
from  south  to  north  is  called  the  moon's  ascending  node, 
while  the  point  of  crossing  from  north  to  south  is  the 
descending  node. 

These  nodes  do  not  remain  fixed,  but  are  in  compara- 
tively rapid  motion,  and  finally  accomplish  an  entire  rev- 
olution around  the  heavens,  on  the  ecliptic.  If,  then, 
we  unite  all  these  facts  it  will  be  seen  that  to  produce  to 
any  observer  an  eclipse  of  the  sun,  the  moon,  at  the  new, 
must  be  exactly  in  one  of  her  nodes,  so  that  the  center 
of  the  moon,  the  node,  and  the  center  of  the  sun,  form  one 


28  T  H  E     S  U  N  . 

and  the  same  straight  line.  Here,  then,  are  the  con- 
ditions precedent  to  a  solar  eclipse.  It  now  remains  to 
BO  follow  these  revolving  orbs  as  to  he  able  to  anticipate 
the  certain  occurrence  of  these  determined  conditions. 
We  follow,  then,  from  night  to  night,  the  waning  moon ; 
she  slowly  approaches  the  sun ;  her  light  becomes  a 
delicate  crescent,  just  visible  in  the  gray  twilight  of 
morning  before  the  rising  of  the  sun ;  at  length  the  moon 
becomes  invisible,  and  when  she  reappears  it  is  on  the 
opposite  Side  of  the  sun,  and  her  silver  crescent  of  light  is 
just  above  the  setting  sun.  There  was  no  eclipse  be- 
cause this  new  moon  did  not  fall  on  the  sun's  path.  It 
is,  however,  easy  to  mark  the  time  of  new  moon,  and 
equally  easy  to  see  and  note  the  time  when  the  moon  is 
in  her  node,  or  on  the  ecliptic,  and  by  thus  watching, 
from  new  moon  to  new  moon,  we  may  see  whether  the 
interval  from  the  passage  of  the  node  up  to  new  moon  13 
growing  shorter,  and  at  what  rate  it  decreases,  till, 
finally,  we  shall  perceive  that  on  the  coming  of  a  cer- 
tain new  moon  it  must  fall  precisely  at  the  node,  and  on 
the  day  of  this  computed  conjunction,  to  him  who  has 
watched,  and  waited,  and  pondered,  and  computed,  the 
sun  must  fade  away  in  total  eclipse.  Such  is  the  train  of 
reasoning  and  observation  which  may  have  first  led  to  the 
resolution  of  this  great  problem,  but  to  whose  genius  we 
are  indebted  for  this  grand  discovery  neither  history  nor 
tradition  furnish  any  information. 

In  consequence  of  the  near  equality  in  the  apparent 
diameters  of  the  sun  and  moon,  and  a  slight  change  in 
both  due  to  a  change  of  the  actual  distance  from  the 
earth  (as  will  be  shown  hereafter),  it  sometimes  happens 
that  the  moon's  diameter  43  less  than  that  of  the  sun. 
When  this  obtains  during  a  solar  eclipse  there  remains 


T  H  E     S  U  H  .  29 

around  the  black  disk  of  the  moon  a  brilliant  ring  of 
solar  light,  and  the  eclipse  is  said  to  be  annular.  When- 
ever the  moon's  center,  at  the  new,  is  not  precisely  at 
the  node,  but  not  so  remote  from  it  as  the  sum  of  the 
semi-diameters  of  those  two  orbs,  there  will  be  a  partial 
obscuration  of  the  sun. 

We  have  presented  these  facts  in  this  place,  as  known 
to  the  early  astronomers,  and  as  admirable  means  of  exer- 
cising the  power  of  thought  on  the  part  of  those  who  may 
desire  to  devote  themselves  to  the1  real  study  of  the  great 
phenomena  of  nature.  We  will  recur  to  this  subject 
again  when  we  shall  have  mastered  the  laws  of  motion 
and  of  gravitation. 

Such  is  a  rapid  survey  of  the  discoveries  of  the  an- 
cients in  the  study  of  that  great  orb,  which,  from  its 
splendor,  even  if  it  be  a  mere  phantom  of  light,  justly 
commands  our  admiration  and  deserves  our  best  efforts 
to  master  its  mysterious  movements  and  its  sublime  phe- 
nomena. 

We  now  proceed  to  exhibit  those  discoveries  which 
could  only  be  accomplished  after  man  had  armed  himself 
with  instruments  of  great  power  and  delicacy,  and  with 
a  vision  increased  a  thousand  fold  beyond  that,  with 
which  he  is  endowed  by  nature. 

DISCOVERIES  OF  THE  MODERNS. — The  rude  instru- 
ments employed  by  the  early  astronomers  sufficed  to  fix 
the  places  of  the  sun  and  the  other  heavenly  bodies  with 
sufficient  accuracy  to  give  a  general  outline  of  the  curves 
they  described,  and  as  these  curves,  as  determined  by 
observation,  approximated  the  circular  form,  it  was  con- 
cluded that  the  deviations  from  that  exact  figure  were 
only  errors  of  observation.  Knowing  the  period  in  which 
the  sun  revolves  round  tha  Jieavens,  and  the  distance  of 


30  THE    SUN. 

the  observer  from  the  center  of  his  assumed  circular  orbit, 
it  was  easy  to  compute  accurately  the  sun's  place  among 
the  stars  on  any  day  of  the  year.  This  computation 
being  made,  no  instrument  then  in  use  could  detect  any 
difference  between  the  computed  place  and  that  actually 
held  by  the  sun.  It  was,  therefore,  unphilosophical  to 
doubt  the  absolute  truth  of  an  hypothesis  thus  sustained 
by  the  best  observations  which  could  then  be  made.  It 
was  not  at  all  difficult  to  observe  roughly  mere  position, 
and  any  error  of  observation  in  fixing  the  place  of  the 
sun  would,  in  the  long  run,  be  eliminated  in  its  effects 
by  taking  into  account  a  large  number  of  revolutions. 
The  degree  of  accuracy  required  in  thus  fixing  the  sun's 
place  among  the  stars  was  widely  different  from  that 
demanded  in  the 

MEASUREMENT  OF  THE  SUN'S  DISTANCE. — The  prin- 
ciples involved  in  the  solution  of  this  great  problem  were 
well  understood  by  the  old  Greek  astronomers,  and  were 
applied  by  them  successfully  in  measuring  the  distances 
of  inaccessible  objects  on  the  surface  of  the  earth.  These 
principles  are  so  simple  that  a  knowledge  of  the  very 
first  rudiments  of  geometry  will  suffice  to  render  intelli- 
gible the  methods  which  are  employed  in  obtaining  the 
data  for  computing  the  distances  of  the  heavenly  bodies. 

Suppose  it  were  required  to  learn  the  distance  of  the 
object  A  from  the  point  C.  From  C  send  to  A  the  visual 
ray  C  A,  then  lay  off  any  line  from  C  B  perpendicular  to 
A  C,  and  measure  its  length.  From  B  draw  the  visual 
ray  B  C,  and  measure  the  angle  C  B  A.  We  have 
thus  formed  a  right-angled  triangle,  in  which  the  angle 
at  C  is  a  right  angle,  the  basej  C  B,  is  known  by  mea- 
surement, and  the  angle  C  B  A  is  known  in  the  same 
way,  hence  may  be  computed,  by  the  simplest  elements 


THE     SUN,  31 

of  trigonometry,  the  length  of  the  distance  C  A,  or  the 
required  quantity. 

Any  error  committed  in  the  measurement  of  the  angle 
C  B  A  grows  more  powerful  in  its  effect  on  C  A,  in  pro- 


portion to  the  number  of  times  C  B  must  be  taken  to 
measure  C  A.  In  our  attempt  to  measure  the  sun's  dis- 
tance we  are  limited  to  a  base  line  equal  in  length  to  the 
earth's  diameter,  and  hence  it  becomes  necessary  to  em- 
ploy every  refinement  of  art  to  eliminate  as  far  as  pos- 
sible the  errors  involved  in  the  measurement  of  the  angle 
C  B  A,  or  its  complement,  the  angle  C  A  B,  on  which, 
iij  the  application  of  these  principles  to  the  problem  in 
question,  depends  the  measurement  of  the  sun's  distance. 
This  quantity  is  the  great  key  which  unlocks  all  the  mys- 
teries of  the  entire  system.  Upon  it  depends  directly 
the  mass,  volume,  and  density  of  the  sun,  the  distances, 
weights,  and  magnitude  of  all  the  planets,  and  even  the 
masses  and  distances  of  the  fixed  stars.  It  is  for  this 
reason  that  modern  science  has  spared  neither  time  nor 


32  T  fl  E     S  U  N  . 

money,  neither  skill  nor  ingenuity  in  the  effort  to  reach 
an  exact  solution  of  this  grand  problem. 

THE  SOLAR  PARALLAX. — In  case  an  observer  were 
located  at  the  sun's  center,  and  from  his  eye  two  visual 
rays  were  drawn,  one  to  the  center  of  the  earth,  the 
other  tangent  to  the  spherical  surface  of  the  earth,  these 
rays  would  form  an  angle  with  each  other  at  the  eye  of 
the  observer,  and  this  angle  is  called  the  surfs  horizontal 
parallax. 


Thus  S  representing  the  sun's  center,  C  the  center  of 
earth,  C  R  a  radius  of  the  earth  perpendicular  to  the 
visual  ray  S  C,  and  S  R  the  visual  ray  drawn  to  the  ex- 
tremity R  of  the  radius,  the  si^le  R  S  C  is  the  solar 
parallax^  and  in  case  it  were  possible  to  measure  that 
angle,  as  the  angle  S  C  R.  is  a  right-angle,  the  remaining 
parts  of  the  triangle  R  S  C  become  known  by  computa- 
tation.  Thus  it  appears  that  the  problem  of  measur- 
ing the  sun's  distance  from  the  earth  resolves  itself  into 
obtaining  the  value  of  the  surfs  horizontal  parallax, 
or  the  angle  under  which  the  earth's  radius  would  be  seen 
from  the  sun's  center. 

No  instruments  have  yet  been  constructed  sufficiently 
delicate  to  accomplish  directly  the  measure  of  this  im- 
portant quantity  with  the  requisite  precision.  But  there 
is  an  indirect  method,  which  has  been  employed  by 
modern  astronomers  to  accomplish  the  same  object,  which 


THE     SUN.  33 

has  been  rewarded  with  satisfactory  success.  This  method 
we  shall  now  proceed  to  explain. 

From  the  most  remote  antiquity  it  has  been  known 
that  there  are  two  planets,  Mercury  and  Venus,  which 
appear  to  revolve  around  the  sun,  never  receding  from 
that  orb  beyond  certain  narrow  and  well  defined  limits. 
The  distances  from  these  planets  to  the  sun  are  less  than 
the  earth's  distance  from  the  same  luminary,  and  hence 
they  must  at  each  of  their  revolutions  pass  between  the 
earth  and  sun.  Modern  science  has  confirmed  these  an- 
cient discoveries,  and  the  telesccpe  has  even  shown  that 
on  certain  rare  occasions  each  of  these  planets  actually 
passes  between  the  solar  disk  and  the  eye  of  an  observer 
on  the  earth,  and  appears  as  a  jc-und  black  spot  on  the 
bright  surface  of  the  sun.  These  passages  of  the  planets 
across  the  solar  disk  are  called  transits,  and  it  happens 
that  the  transits  of  Venus  furnish  an  admirable  means 
of  reducing  the  errors  involved  in  the  direct  measure- 
ment of  the  solar  parallax,  as  we  shall  now  proceed  to 
explain. 

We  will  first  present  the  principle  involved,  and  then 
make  the  application. 

Let  it  be  required  to  determine  the  distance  of  the 
point  A  from  any  inaccessible  surface,  as  C  D,  and  that 
A  A'  is  the  longest  base  line  which  can  possibly  be  em- 
ployed. In  case  the  distance  of  the  point  B'  on  the  sur- 
face C  D  be  required,  then  the  angles  B'  A!  A  and  B'  A  A' 
must  be  measured,  and  their  sum,  subtracted  from  180°, 
gives  for  a  remainder  the  angle  A  B'  A',  or  the  angle 
under  which  the  line  A  A!  would  be  seen  by  a  spectator 
at  B'.  Now  this  angle,  because  of  its  minute  value,  may 
be  difficult  to  measure,  and  we  desire  to  nnd  some  arti- 
fice by  which  this  difficulty  may  be  at  least  diminished, 

2* 


8-4 


THE     SUN 


if  not  entirely  removed.  Suppose  then  a  material  point 
to  be  located  at  B,  much  nearer  to  A  A'  than  to  C  D,  an 
observer  at  A  would  see  the  point  B  projected  on  C  D  at 
B",  while  an  observer  at  A'  would  see  the  same  point 


D 


projected  at  B'.  Now  let  us  suppose  that  the  points  B' 
and  B"  can  be  identified  and  seen  as  round,  black,  perma- 
nent spots  on  the  remote  surface  C  D ;  in  case  B  is  fur- 
ther from  C  D  than  from  A  A',  it  is  clear  that  the  visual 
angle  subtended  by  B7  B",  as  seen  from  A,  will  be  larger 
than  the  visual  angle  subtended  by  A  A',  as  seen  from  B', 
in  the  proportion  of  the  distance  B  B'  to  the  distance  B  A' ; 
and  if  B  B7  should  be  2|  times  longer  than  B  A',  then 
would  B'B"  be  2^  times  longer  than  A  A';  and  the  prob- 
lem resolves  itself  into  the  measurement  of  the  large 
angle  B'  A  B"  instead  of  the  small  angle  A  B'  A'. 

Such  is  the  principle  ;  and  we  will  now  proceed  to  its 
application.  A  A'  is  the  diameter  of  the  earth.  B  is  the 
planet  Venus,  and  C  D  is  a  diameter  of  the  solar  disk. 
To  an  observer  at  A,  Venus  is  seen  on  the  sun  as  a  black 
spot  at  B",  while  an  observer  at  A!  sees  the  planet  pro- 


THE     SUN* 


35 


jected  at  B'.  Venus  is  about  2|  times  further  from  the 
sun  than  from  the  earth,  hence  B  B'  is  2^  times  longer 
than  B  A',  and  therefore  B'  B"  is  2^  times  greater  than 
A  A',  or  2i  times  greater  than  the  diameter  of  the  earth, 
as  seen  from  the  sun,  or  Jive  times  greater  than  the  sun's 
horizontal  parallax ;  it  is  therefore  but  one  fifth  part  as 
difficult  to  measure  the  angle  B'AB"  as  to  measure  the 
angle  A  B'  A'. 

There  is  another  important  advantage  gained  in  using 
the  transit  of  Vtnus  in  the  measurement  of  the  solar 
parallax,  arising  from  the  fact  that  modern  science  has 
obtained  a  ver y  exact  knowledge  of  the  relative  velocity 
of  Venus  across  the  solar  disk. 


If  we  note,  then,  exactly  the  moment  the  planet  is  in 
contact  with  the  solar  disk  at  p,  and  also  at  p',  this  inter- 
val of  time  will  give  an  enlarged  measure  of  the  chord  pp', 
described  by  the  planet  as  seen  from  the  station  A.  In 
like  manner  the  observer  at  K  making  the  same  observa- 


36  THE     SUN. 

tions  at  q  and  q',  we  shall  obtain  the  relative  lengths  of  these 
two  chords,  and  hence  an  accurate  measure  of  the  inter- 
val B'  B",  by  which  they  are  separated,  or  of  five  times 
the  solar  parallax. 

Although  this  problem  may  appear  somewhat  complex 
at  the  first,  careful  study  will  render  it,  in  these  general 
outlines,  very  simple  and  easily  intelligible.  Its  high 
value  in  the  measurement  of  the  very  most  important  ele- 
ment in  the  entire  system  of  the  sun  and  his  satellites 
should  secure  from  the  student  all  the  time  and  attention 
necessary  to  its  complete  mastery. 

Such  is  the  importance  attaching  to  this  great  problem, 
that  at  the  last  transit  of  Venus,  governmental  expedi- 
tions were  fitted  out  at  great  expense,  and  observers  were 
dispatched  to  points  on  the  earth's  surface  as  far  asunder 
as  possible,  each  observer  noting,  with  every  precaution, 
the  exact  time  in  hours,  minutes,  and  seconds,  from  the 
first  contact  of  the  planet  with  the  sun's  disk,  up  to  the 
moment  of  last  contact. 

It  will  be  seen  that  the  problem,  as  presented  above, 
is  freed  from  many  complications  which  surround  it  in 
practice,  such  as  those  arising  from  the  revolution  of 
the  earth  in  its  orbit,  its  rotation  on  its  axis,  and  the 
fact  that  the  observers  are  not  located  at  the  extremities 
of  the  same  diameter  of  the  earth.  These  and  other 
matters  aflecting  the  result  being  carefully  taken  into 
account,  we  have  obtained,  for  the  value  of  the  sun's  hori- 
zontal  j>arallax,  when  at  his  mean  distance  from  the 
earth,  8 ".6,  or  eight  and  six- tenths  seconds  of  arc, 
showing  that  this  grand  orb  is  removed  from  the  earth  to 
a  distance  cf  about  ninety- five  millions  of  miles. 

We  shall  recur  to  the  transits  of  Mercury  and  Venus 
when  we  come  to  treat  of  those  bodies. 


THE     SUN'S    LIMB 


SOLAR     SPOTS 


THE     SUN.  87 

THE  SUN'S  REAL  MAGNITUDE. — Modern  instruments 
enable  us  to  measure  with  great  exactitude  the  angle 
subtended  by  the  sun's  apparent  diameter,  an  angle  whose 
value  at  the  sun's  mean  distance  amounts  to  32'  .V. 
But  a  globe  removed  to  a  distance  of  ninety-five  mil- 
lions of  miles,  and  yet  having  an  apparent  diameter 
of  32 '.I",  must  have  a  real  diameter  of  no  less  than 
882,000  miles  in  length,  or  more  than  one  hundred  and 
eleven  times  longer  than  the  diameter  of  our  earth,  as  we 
shall  hereafter  see.  This  enables  us  to  compare  the  bulk 
or  volume  of  these  two  globes,  and  we  find  that  it  would 
require  no  less  than  one  million  three  hundred  and  eighty- 
four  thousand  four  hundred  and  seventy-two  globes  as 
large  as  the  earth  to  fill  the  vast  interior  of  a  hollow 
globe  as  large  as  the  sun.  This  is  a  comparison  of  bulk 
only  ;  the  relative  weights  of  the  earth  and  sun  must  be 
considered  hereafter. 

If  this  wonderful  globe  excited  our  admiration  by  the 
splendor  of  its  surface,  and  its  floods  of  light  and  heat, 
how  must  this  admiration  be  increased  when  we  contem- 
plate its  great  distance  and  its  gigantic  proportions  ? 

THE   PHYSICAL   CONSTITUTION   OF   THE   SUN. — But  for 

the  aid  derived  from  the  telescope  man  could  never  have 
passed  beyond  mere  conjecture  as  to  what  lies  on  the  sur- 
face of  the  sun.  The  telescope,  however,  'magnifying  a 
thousand  times,  transports  the  observer  over  a  vast  pro- 
portion of  the  distance  separating  him  from  the  solar  orb, 
and  plants  him  in  space  within  ninety-five  thousand  miles 
of  the  sun's  surface,  there  to  examine  the  phenomena  re- 
vealed to  his  sight  by  this  magic  tube.  We  may,  there- 
fore, regard  the  suu's  distance  as  reduced  to  the  thou- 
sandth part  of  its  actual  value,  and  we  should  not  be 
surprised  to  find  upon  a  globe  of  such  grand  proportions 


38  T  H  E     S  U  N  . 

fluctuations  and  changes  which,  at  this  reduced  distance, 
may  become  distinctly  visible.  This  anticipation  has  not 
been  disappointed. 

THE  SOLAR  SPOTS. — To  the  naked  eye  the  sun's  sur- 
face presents  a  blaze  of  insufferable  splendor,  and  even 
when  this  intense  light  is  reduced  by  the  use  of  any 
translucent  medium,  the  entire  disk  appears  evenly 
shaded,  with  a  slight  diminution  of  light  around  the  cir- 
cumference, but  without  visible  spot  or  variation.  When, 
however,  the  power  of  vision  is  increased  a  hundred  or  a 
thousand  fold  by  telescopic  aid,  and  when  the  intense 
heat  of  the  sun  and  his  equally  intense  light  are  reduced 
by  the  interposition  of  deeply  colored  glasses,  the  eye  re- 
cognizes a  surface  of  most  wonderful  character.  Instead 
of  finding  the  sun  everywhere  equally  brilliant,  the  tele- 
scope shows  sometimes  on  its  surface  black  spots,  of  very 
irregular  figure,  jagged  and  broken  in  outline,  and  sur- 
rounded by  a  penumbra  conforming  in  figure  to  the  gen- 
eral outline  of  the  central  black  spot  (called  the  nucleus,) 
but  of  much  lighter  shade.  Even  where  there  are  no 
spots,  the  surface  of  the  sun  is  by  no  means  uniformly 
brilliant.  The  entire  surface  has  a  mottled  appearance, 
with  delicate  pores  or  points,  no  one  of  which  can  be 
readily  held  by  the  eye,  but  a  group  of  them  may  some- 
times be  seized  by  the  vision  under  favorable  atmospheric 
circumstances,  and  can  be  held  long  enough  to  demon 
strate  that  these  minute  pores  do  not  change  their  relative 
position,  or  disappear  while  under  the  eye. 

Besides  the  mottling  of  the  surface,  the  telescope  de- 
tects in  the  solar  orb  a  variety  of  brighter  streaks,  called 
faculcBj  whose  appearance  has  been  connected,  as  some 
believe,  with  the  breaking  out  of  the  black  spots. 

Watching  from  day  to  day  a  single  spot,  or  a  group 


T  H  E    s  u  sr .  39 

of  spots,  on  the  sun's  surface,  they  are  found  to  advance 
together  in  the  same  direction,  slowly  to  approach  the 
edge  of  the  sun,  finally  to  disappear  from  the  sight,  and 
after  a  certain  number  of  days  to  re-appear  on  the  op- 
posite side  of  the  sun's  disk,  revealing  the  surprising 
fact  that  the  sun  is  slowly  rotating  on  an  axis  whose 
position  seems  to  be  invariable.  In  case  these  spots  were 
absolutely  fixed  on  the  sun's  surface,  they  would  reveal 
the  exact  period  in  which  his  rotation  is  performed,  but 
in  consequence  of  their  change  of  figure,  and  change  of 
position  as  well,  we  can  only  reach  an  approximate  value 
of  the  period  of  rotation.  This  is  now  fixed,  by  the  best 
authorities,  at  twenty-Jive  days,  eight  hours  and  nine 
minutes. 

During  the  past  thirty  years  M.  Schwabe,  of  Dessau, 
has  given  special  daily  attention  to  counting  the  groups 
and  spots  on  the  sun,  and  by  preserving  a  record  it  has 
been  discovered  that  the  amount  of  solar  surface  covered 
by  the  black  spots  is  not  only  variable  but  that  period- 
icity marks  this  variation.  The  entire  change,  from  a 
maximum  of  spots  counted  in  any  year,  to  the  mini- 
mum, occupies  about  five  and  a  half  years,  and  the  same 
time  elapses  from  a  minimum  to  a  maximum,  making 
the  period  from  maximum  to  maximum  eleven  years. 
This  fact  is  one  of  the  most  surprising  revealed  in  the 
physical  constitution  of  any  of  the  heavenly  bodies,  and 
thus  far  has  baffled  the  power  of  human  investigation  to 
explain  it,  while  its  mysterious  character  is  increased  by 
the  fact  recently  discovered,  that  this  periodicity  in  the 
solar  spots  is  identical  in  duration  with  a  certain  varia- 
tion observed  in  the  intensity  of  terrestrial  magnetism. 
Thus,  it  would  seem,  that  a  new  bond  of  union  is  about 
to  be  established  between  the  earth  we  inhabit  and  that 


40  T  H  E     S  U  N 

mighty  orb  whence  we  receive  our  supplies  of  light,  and 
heat. 

Some  astronomers  account  for  the  solar  spots  by  sup- 
posing the  sun  to  be  a  solid,  dark,  opaque  globe,  sur- 
rounded by  two  atmospheres,  the  exterior  one  a  highly 
luminous  and  gaseous  envelope,  the  interior  more  dense, 
and  possessing  great  reflecting  power.  The  spots  are 
supposed  to  result  from  powerful  internal  convulsions, 
upheavals  from  within  breaking  through  these  two  en- 
velopes, and  producing  a  more  extended  chasm  in  the 
external  luminous  atmosphere.  I  have  examined  the  sur- 
face of  the  sun  and  closely  observed  the  large  solar  spots 
with  a  refractor  of  admirable  performance,  and  so  far 
from  presenting  an  appearance  such  as  the  above  hypoth- 
esis would  warrant,  the  entire  exhibition  resembled  the 
openings  often  found  by  melting  through  a  thick  stratum 
of  solid  ice  from  below — the  spiky  and  jagged  outline  of 
the  black  nucleus  being  well  represented  by  a  similar 
form  in  the  opening  through  the  ice,  while  the  penumbra 
was  very  faithfully  represented  by  the  thinner  portions 
of  ice  remaining  around  the  opening.  It  is  not  to  be  in- 
ferred from  this  comparison  that  the  author  entertains 
the  opinion  that  the  exterior  of  the  sun  is  a  solid  crust, 
and  that  these  solar  spots  are  produced  from  the  melting 
of  this  crust  by  the  action  of  internal  fires.  The  com- 
parison is  made  for  the  purpose  of  illustrating,  as  strongly 
as  possible,  the  absolute  appearance  of  these  inexplicable 
phenomena,  and  to  present  as  strong  a  contrast  as  the 
facts  warrant  to  the  statement  made  by  a  distinguished 
astronomer,  that  the  sun's  surface,  when  viewed  by  a 
powerful  telescope,  resembles  "the  subsidence  of  some 
floculent  chemical  precipitates  in  a  transparent  fluid.'7 
So  far  from  this  being  the  case,  the  sharp  outlines  of  the 


Of  THE 

•UNIVERSfT 

41 

penumbra  surrounding  the  dark  spots  have  often  been  seen, 
to  cut  directly  across  the  minute  pores,  dividing  them 
sharply  and  sometimes  equally. 

Recent  observations  seem  to  demonstrate  that  what  has 
generally  been  considered  the  solar  surface  is  really  the 
exterior  of  a  cloudy  atmosphere  beneath  the  luminous 
ocean  surrounding  the  sun.  Mr.  Dawes,  by  an  eye-piece 
of  his  own  construction,  bearing  a  metallic  diaphragm, 
in  which  a  minute  hole  is  pierced,  coincident  with  the 
axis  of  the  telescope,  has  been  enabled  to  make  a  very 
critical  examination  of  the  solar  spots.  He  finds  in  the 
center  of  the  dark  spot  a  smaller  opening,  which  is,  as 
now  seen,  intensely  black,  and  this  is  at  present  regarded 
as  the  real  surface  of  the  solar  orb.  The  same  distin- 
guished observer  has  announced  the  discovery  of  an  actual 
rotation  of  the  solar  spots  about  a  central  axis.  This 
important  fact  has  given  rise  to  speculation  as  to  the 
probable  cause  of  these  wonderful  fluctuations  which  occur 
in  the  solar  atmospheres. 

It  is  conjectured  that  these  exhibitions  may  be  pro- 
duced by  tremendous  storms  or  whirlwinds  resembling 
those  which  sometimes  sweep  over  the  surface  of  the 
earth,  and  whose  vortices,  if  seen  from  above,  would 
present  an  appearance  not  unlike  the  spots  on  the  sun. 
We  understand  how  these  tornadoes  are  generated  in  the 
atmosphere  of  the  earth,  but  it  is  useless  to  attempt  to 
conjecture  the  causes  which  can  produce  such  amazing 
effects  in  the  sola?  atmosphere. 

INTENSITY  OF  THS  SOLAR  HEAT. — Admitting  that 
the  heat  of  the  sun  falling  on  tha  earth  is  diminished  in 
the  ratio  of  the  square  of  the  sun's  distance,  it  is  not  diffi- 
cult to  form  some  approximate  idea  of  the  intensity  of  the 
solar  heat  at  the  surface  of  the  sun.  By  exposing  a  sur- 


42  T  H  E      S  U  N  . 

face  of  ice  to  the  direct  action  of  the  sun's  heat,  when  the 
sun  was  nearly  vertical,  Sir  John  Herschel  determined 
•by  experiment  the  thickness  of  the  ice  melted  in  a  given 
time. 

From  this  and  like  experiments  it  is  determined  that  it 
would  require  the  combustion  of  more  than  one  hundred 
and  thirty  thousand  pounds  of  coal  per  hour  on  each 
square  foot  of  the  sun's  surface  to  produce  a  heat  equal 
to  that  radiated  from  the  solar  orb. 

When  an  image  of  the  sun  is  received  on  any  surface 
it  is  found  that  the  central  point  of  the  image  is  more 
heated  than  the  parts  near  the  circumference,  and  that 
the  temperature  diminishes  from  the  equator  toward  the 
poles. 

THE  SUN'S  ATMOSPHERE. — These  facts  have  been  ac- 
counted for  by  supposing  the  sun  to  be  surrounded  by  a 
dense  atmosphere,  and  that  the  heated  rays  which  pass 
through  the  deepest  part  of  this  atmosphere  lose  a  por- 
tion of  their  heat,  and  hence  the  regions  around  the  disk 
of  the  sun  should  be,  to  tis;  less  heated  than  those  near 
the  center  of  the  solar  orb.  There*  are  some  phenomena 
attending  a  total  eclipse  of  the  sun  which  seem  to  sustain 
this  hypothesis  of  a  solar  atmosphere.  At  the  moment 
the  eclipse  becomes  total,  there  is  seen  to  burst  from  the 
jet  black  disk  of  the  moon  a  sort  of  halo  or  glory,  radia- 
ting on  every  side,  and  presenting  a  spectacle  of  won- 
derful grandeur,  so  much  so  that  on  the  occasion  of  the 
eclipse  of  July,  1842,  witnessed  at  Pavia,  the  entire 
populace  burst  into  a  shout  of  wonder  and  admiration. 

There  also  appeared,  at  the  same  time,  flames  of  fire 
darting  from  behind  the  limb  of  the  moon,  resembling 
mountains  of  rose-colored  light,  rising  to  the  height  of 
forty  or  fifty  thousand  miles  above  the  surface  of  the  sun. 


T  H  E     S  U  N  .  43 

These  flames  are  known  to  assume  the  form  of  cloudy 
exhalations  which,  in  some  instances,  seem  to  be  drifted 
like  smoke  ascending  in  a  calm  atmosphere  to  a  certain 
level,  where  it  meets  a  current  and  is  borne  off  horizon- 
tally. 

There  is  another  phenomenon  attending  the  rising  and 
setting  of  the  sun  at  certain  seasons  of  the  year  in  the 
shape  of  a  vast  beam  of  faint,  gauzy  light,  of  lenticukr 
form,  rising  from  the  point  of  sunset  in  the  evening,  and 
stretching  upward  in  the  direction  of  the  sun's  path  some- 
times 70°  or  80°.  This  is  called  the  Zodiacal  Light, 
and  has  long  been  regarded  as  the  evidence  of  uncon- 
densed  nebulosity,  or  a  material  atmosphere  surrounding 
the  equatorial  regions  of  the  sun.  The  central  line,  or 
axis,  of  this  luminous  beam  does  not  appear  to  be  fixed 
in  position,  and  hence  a  difficulty  arises  not  readily  re- 
moved by  the  hypothesis  of  a  material  atmosphere. 

Some  have  supposed  this  mysterious  luminous  zone  to 
be  a  nebulous  ring  surrounding  our  moon,  while  others 
have  regarded  it  as  an  immense  ring  of  minute  asteroids 
or  meteors,  revolving  round  the  sun,  and  slowly  subsid- 
ing into  this  grand  luminary,  and  by  the  conversion  of 
their  velocity  into  heat,  as  they  fall  in  a  perpetual  shower 
on  the  sun,  or  are  burned  up  in  the  solar  atmosphere, 
keeping  up  a  supply  equal  to  the  vast  radiation  shot  forth 
from  the  sun  at  every  moment  of  time.  While  we  are 
willing  to  admit  that  a  material  globe,  falling  into  the 
solar  atmosphere,  may  generate  immense  heaf,  in  pro- 
portion to  its  magnitude  and  velocity,  it  seems  quite  im- 
possible to  adopt  the  hypothesis  that  the  zodiacal  light  is 
either  a  material  solar  atmosphere  or  a  ring  of  revolving 
meteors,  as  it  extends  to  such  a  vast  distance  from  the 
sun,  that  if  revolving  with  the  sun,  as  does  our  atmo- 


44  T  H  E     S  U  N . 

sphere  with  the  earth,  the  particles  would  be  thrown  be- 
yond the  control  of  the  sun  and  would  be  dissipated  into 
space. 

We  are  compelled  to  acknowledge  that  up  to  the  pres- 
ent time  science  has  rendered  no  satisfactory  account  of 
the  origin  of  the  solar  light  or  heat.  Whence  comes  the 
exhaustless  supply,  scattered  so  lavishly  into  space  in 
every  direction,  we  know  not.  Neither  is  it  possible  to 
give  a  satisfactory  solution  of  the  solar  spots,  or  of  any 
of  the  strange  phenomena  attending  their  rotation  or 
translation  on  the  sun's  surface.  The  idea  that  torna- 
does and  tempests  rage  in  the  deep,  luminous  ocean  that 
surrounds  the  sun,  like  those  which  sometimes  agitate 
the  atmosphere  of  the  earth,  has  no  solid  foundation. 
We  know  the  exciting  causes  of  the  tornadoes  on  earth, 
but  why  such  storms  should  exist  in  the  solar  photosphere 
it  is  in  vain  to  conjecture  at  present.  Doubtless  the  time 
will  come  when  these  phenomena  will  be  explained.  Per- 
severing and  well-directed  observation  will,  in  the  end, 
triumph  ;  but  these  are  matters  which  must  be  consigned 
to  the  researches  of  posterity. 


CHAPTER    II. 

MERCURY,   THE   FIRST    PLANET  IN  THE    ORDER  OF  DIS- 
TANCE  FROM  THE  SUN. 

ITS  EARLY  DISCOVERT. — DIFFICULT  TO  BE  DISTINGUISHED  FROM  THE  STARS.— 
ELONGATIONS.— MOTION  DIRECT  AND  RETROGRADE.— SOMETIMES  STATIONARY. 
—NATURE  OF  THK  ORBIT.— VARIATION  IN  THE  ELONGATION  EXPLAINED.— 
THE  No  DPS.— TRANSIT  OP  MERCURY.— INCLINATION  OP  MERCURY'S  ORBIT.— 
MEAN  DISTANCE  FROM  THE  SUN. — CONJUNCTIONS. — PHASES. — DIAMETER  AND 

VOLUMK. 

No  discovery  made  by  the  ancients  gives  us  a  higher 
idea  of  the  care  and  scrutiny  with  which  their  astronom- 
ical observations  were  conducted  than  the  fact  that  the 
minute  planet  Mercury,  so  difficult  to  be  seen,  and  so  un- 
distinguishable  from  the  fixed  stars,  was  discovered  in 
the  very  earliest  ages  of  the  world.  That  the  brighter 
planets,  such  as  Venus  and  Jupiter,  whose  brilliancy  ex- 
ceeds that  of  any  of  the  fixed  stars,  should  have  been 
detected  to  be  wandering  bodies,  even  in  the  remotest 
antiquity,  is  by  no  means  surprising.  For  in  watching 
the  sun  rising  and  the  sun  setting,  so  as  to  note,  in  the 
first  instance,  the  stars  nearest  to  the  sun,  which  were 
the  last  to  fade  away,  and  in  the  second,  those  stars  which 
were  the  first  to  become  visible,  the  change  of  position 
of  the  planets  Venus  and  Jupiter  could  not  fail  to  attract 
the  attention  of  the  student  of  the  heavens ;  but  the 
planet  Mercury  is  so  small,  and  so  rarely  visible,  even  to 
the  keenest  eye,  that  it  is  said  Copernicus  himself,  during 
his  whole  life,  devoted  to  the  study  of  the  heavens,  never 
once  caught  sight  of  this  almost  invisible  world. 


46  MERCURY. 

Mercury,  in  his  appearance  to  the  naked  eye,  is  not 
distinguishable  from  the  fixed  stars.  His  close  proximity 
to  the  sun,  the  fact  that  he  is  never  visible  except  near 
the  horizon,  and  the  intense  brilliancy  of  his  disk  give  to 
him  that  twinkling  appearance  which  distinguishes  the 
fixed  stars.  Notwithstanding  all  these  difficulties  the 
oldest  astronomers  managed  to  acquire  a  very  complete 
knowledge  of  the  principal  facts  connected  with  the 
movement  of  this  planet.  By  a  careful  and  continuous 
examination  it  was  found  that  Mercury  never  receded 
more  than  about  twenty  degrees  from  the  sun's  center. 
The  amount  of  recess,  or  elongation  as  it  is  called,  was 
soon  discovered  to  be  a  variable  quantity,  a  fact  which 
demonstrated  that  in  case  the  planet  revolved  in  a  circu- 
lar orbit,  inclosing  the  sun,  the  sun  could  not  occupy  the 
center  of  this  circle.  By  watching  the  elongations  from 
revolution  to  revolution,  it  was  found  that  they  varied 
from  a  minimum  of  16°  12',  to  a  maximum  of  20°  48'. 
Knowing  the  amount  of  this  variation,  and  watching 
carefully  the  progressive  change,  it  became  possible  to 
reach  a  tolerably  accurate  knowledge  of  the  nature 
of  the  orbit  described  by  the  planet  in  its  revolution 
around  the  sun.  It  was  soon  discovered  that  in  some 
portions  of  his  orbit  Mercury  advanced  with  the  sun  in 
his  march  among  the  fixed  stars,  while  in  other  parts 
of  his  orbit  his  motion  became  retrograde,  and  in  the 
change  from  direct  to  retrograde,  and  the  reverse,  the 
planet  apparently  ceased  to  move,  and  for  a  short  time 
became  stationary. 

It  will  be  seen  that  all  these  changes  are  readily  ac- 
counted for  by  supposing  the  planet  to  revolve  about  the 
Bun  in  a  circular  orbit,  the  sun  being  eccentrically  placed. 
If  we  conceive  two  visual  rays,  to  be  drawn  from  the  eye 


MERCURY.  47 

of  the  observer,  and  tangent  to  the  orbit  of  Mercury  on 
the  right  and  on  the  left,  the  planet,  while  traversing  that 
arc  of  its  orbit  intercepted  between  the  points  of  contact 
and  nearest  to  the  eye,  will  move  direct ;  in  passing 
through  the  point  of  contact  after  direct  motion  ceases,  it 
will  move  off  in  the  direction  of  the  visual  ray,  and  hence 
will  appear  stationary  for  a  short  time.  In  the  larger 
portion  of  its  orbit  (that  remote  from  the  eye)  its  motion 
must  be  opposite  to  that  of  the  sun,  and  hence  retro- 
grade. In  coming  up  to  the  second  point  of  contact  the 
planet  will  move  along  the  visual  ray  toward  the  eye  of 
the  observer,  and  hence  for  a  short  time  will  appear 
stationary. 

To  account  for  the  variation  in  the  elongations  of 
Mercury,  we  must  either  suppose  the  point  of  nearest 
approach  of  the  planet  to  the  sun,  called  its  perihelion, 
to  be  in  motion,  or  else  we  must  suppose  the  spectator  to 
be  himself  moving,  and  thus  to  behold  the  planet,  its 
perihelion  point,  and  the  sun,  under  varying  relations  to 
each  other.  As  the  early  astronomers  assumed  the  im- 
mobility of  the  earth,  they  explained  the  variations  in 
the  elongations  of  Mercury  by  giving  to  its  perihelion 
point  a  motion  of  revolution  about  the  sun. 

It  is  impossible  to  follow  the  planet  with  the  naked 
eye  in  its  close  approach  to  the  solar  orb,  as  its  feeble  re- 
flected light  is  necessarily  overpowered  by  the  brilliancy 
of  the  sun,  but  by  close  observation,  and  by  marking  the 
positions  of  the  planet  at  its  disappearance  and  reappear- 
ance, the  old  astronomers  are  said  to  have  reached  to  a 
knowledge  of  the  fact  that  this  planet  sometimes  crosses 
the  sun's  disk,  producing  what  is  called  a  transit  of 
Mercury,  identical  in  its  phenomena  with  the  transit 
of  Venus,  already  spoken  of  in  connection  with  the  de- 


X 

48  MERCURY. 

termination  of  the  solar  parallax.  In  case  the  plane  of 
the  orbit  of  Mercury  were  exactly  coincident  with  the 
plane  of  the  sun's  apparent  orbit,  it  is  manifest  that  every 
revolution  of  the  planet  would  produce  a  transit.  As 
this,  however,  is  not  the  case,  and  as  no  central  transit 
can  occur,  except  when  the  planet  crosses  the  visual  ray 
drawn  from  the  eye  of  the  observer  to  the  sun's  center, 
it  is  manifest  that  the  planet  Mercury,  during  a  central 
transit,  must  actually  pass  through  the  ecliptic  from  one 
side  of  this  plane  to  the  other.  This  point  of  passage 
through  the  plane  ef  the  sun's  apparent  orbit  is  called 
the  node  of  the  planet's  orbit.  There  are,  of  course, 
two  such  points.  The  planet  passes  its  descending  node 
in  moving  from  the  north  to  the  south  side  of  the  ecliptic, 
and  its  ascending  node  on  its  return  from  the  south  to 
the  north  side. 

It  is  thus  seen  that  in  order  to  produce  a  transit  of 
Mercury  there  must  be  a  conjunction  of  the  planet,  ita 
node,  and  the  sun.  Whenever  this  conjunction  is  abso- 
lute, Mercury  will  pass  across  the  sun's  center.  When 
it  is  only  approximate,  the  planet  will  transit  a  small 
portion  of  the  sun's  disk,  or  possibly  pass  without  contact 
at  all. 

An  attentive  examination  of  the  places  of  the  planet, 
before  and  after  a  transit,  led  to  a  pretty  accurate  de- 
termination of  the  ?,ngle  under  which  the  plane  of  the 
planet's  orbit  is  inclined  to  the  plane  of  the  ecliptic.  This 
angle  was  approximately  determined  by  the  ancients, 
while  modern  science  fixed  it  at  the  commencement  of 
the  present  century  at  70.00'.10". 

The  motion  of  Mercury  in  its  orbit  is  more  rapid  than 
that  of  any  of  the  planets  thus  far  discovered,  traveling, 
as  it  does,  more  than  one  hundred  thousand  miles  an  hour, 


MERCURY.  49 

and  performing  its  entire  revolution  about  the  sun  in  about 
eighty-eight  of  our  days.  In  case  this  world  has  the 
same  variety  of  seasons  which  mark  the  surface  of  our  own 
earth,  these  will  follow  each  other  in  such  rapid  succession 
that  the  longest  of  them  will  consist  of  only  about  three 
of  our  weeks.  It  is  not  difficult  to  compute  the  intensity 
of  solar  light  and  heat  which  falls  upon  the  surface  of 
the  planet  Mercury,  in  case  these  be  subjected  to  the 
same  modifying  influences  which  exist  upon  the  earth. 
But  as  we  remain  in  ignorance  of  the  circumstances 
•which  surround  this  distant  planet,  it  is  vain  to  specu- 
late upon  the  physical  constitution  of  a  world  whose  close 
proximity  to  the  sun  has  thus  far  shut  it  out  from  the 
reach  of  telescopic  examination. 

The  distance  of  the  planet  Mercury  from  the  sun  may 
be  readily  determined,  in  certain  portions  of  its  orbit,  in 
case  we  know  first  the  earth's  distance  from  the  same 
orb.  For  example,  conceive  a  visual  ray  to  be  drawn 
from  the  earth,  tangent  to  the  orbit  of  Mercury  (sup- 
posed, for  the  present,  to  be  circular)  ;  place  the  planet 
at  the  point  of  contact,  and  join  the  center  of  the  planet 
with  the  center  of  the  sun  ;  also  join  the  centers  of  the 
earth  and  sun — the  triangle  thus  formed,  having  the 
earth,  Mercury,  and  the  sun  as  the  vertices  of  its 
three  angles  is  right-angled  at  Mercury,  while  the  angle 
at  the  earth  is  readily  measured,  and  is  nothing  more, 
indeed,  than  the  elongation,  for  the  time  being,  of  that 
planet.  Hence,  in  the  right  angled-triangle,  we  know 
the  angles  and  the  longest  side,  extending  from  the  earth 
to  the  sun,  and  by  the  simplest  principles  of  trigonom- 
etry, we  can  compute  the  remaining  parts — namely, 
the  distance  of  Mercury  from  the  sun  and  from  the  earth. 
By  this,  and  by  other  methods  more  accurate,  it  is  found 

3 


^0  MERCURY. 

that  Mercury  revolves  in  an  orbit  around  the  sun,  and 
at  a  mean  distance  of  about  thirty-six  millions  of  miles. 

As  the  entire  orbit  of  this  planet  lies  within  the  limits 
already  assigned,  it  follows  that  the  planet  can  never  be 
seen  in  a  quarter  of  the  heavens  opposite  to  the  sun,  or 
can  never  be  in  opposition.  When  nearest  the  earth,  and 
on  the  right  line  joining  the  sun  and  earth,  Mercury  is 
said  to  be  in  inferior  conjunction.  When  180°  distant 
from  this  place  it  is  on  the  other  side  of  the  sun,  with 
respect  to  the  earth,  and  is  then  in  its  superior  conjunc- 
tion. 

The  telescope  has  demonstrated  that  this  planet  passes 
through  changes  like  those  presented  by  the  moon.  When 
in  superior  conjunction  the  planet  will  be  seen  nearly 
round,  as  in  that  position  nearly  the  whole  of  the  illu- 
minated surface  is  turned  toward  the  eye  of  the  observer 
on  the  earth.  As  the  planet  comes  round  to  its  inferior 
conjunction  the  light  gradually  wanes,  until  at  inferior 
conjunction  a  slender  crescent  of  great  delicacy  and  beauty 
is  revealed  to  the  eye,  provided  the  planet  does  not  lose 
its  light  entirely  in  the  passage  across  the  sun's  disk. 
These  phases  of  Mercury  prove,  beyond  question,  the  fact 
that  the  planet  does  not  shine  by  its  own  light,  but  that 
its  brilliancy  is  derived  from  reflecting  the  light  of  the 
solar  orb. 

The  degree  of  precision  reached  in  predicting  the 
transits  of  Mercury  indicates,  with  wonderful  force,  the 
progress  of  modern  astronomy.  The  first  predicted 
transit  which  was  actually  observed  occurred  in  1631, 
when  the  limits  of  possible  error  were  fixed  by  the  com- 
puter at  four  days ;  and  hence  the  watch  commenced 
two  entire  days  before  the  predicted  time. 

If  the  transit  had  taken  place  in  the  night  time,  the 


MERCURY.  51 

opportunity  for  verification  would  have  been  lost.  For- 
tunately this  was  not  the  case,  and  the  toil  and  zeal  of 
Gassendi  were  rewarded  with  the  first  view  of  Mercury 
projected  on  the  solar  disk  ever  witnessed  by  mortal  man. 
Nearly  two  hundred  years  later,  at  the  beginning  of  the 
nineteenth  century,  the  French  astronomers  ventured  to 
assert  that  their  predictions  could  not  be  in  error  more 
than  forty  minutes.  The  transit  which  occurred  on  the 
8th  Nov.,  1802,  verified  this  assertion  very  nearly.  By 
a  more  careful  study  of  the  causes  affecting  the  place  of 
the  planet,  forty- three  years  later,  the  discrepancy  between 
computation  and  observation  was  reduced  to  only  sixteen 
seconds  of  time,  a  quantity  very  minute,  when  we  take 
into  account  the  variety  of  causes  affecting  the  resolu- 
tion of  the  problem.  The  transits  of  Mercury  recur  at 
certain  regular  intervals,  repeating  themselves  after  a 
cycle  of  217  years,  falling  for  the  present  in  the  months 
of  May  and  November. 

Having  learned  the  distance  of  Mercury  from  the  earth, 
and  having  measured  the  angle  subtended  by  its  diameter, 
we  find  its  actual  magnitude  to  be  much  smaller  than 
that  of  the  earth.  Its  diameter  is  but  3,140  miles,  and 
its  volume  is  but  0.063,  the  earth's  volume  being  counted 
as  unity. 

In  comparison  with  the  vast  proportions  of  the  sun, 
this  little  planet  sinks  into  absolute  insignificance,  for  if 
the  sun  be  divided  into  a  million  equal  parts  Mercury 
would  not  weigh  as  much  as  the  half  of  one  of  these 
parts. 


CHAPTER    III. 

VENUS,    THE   SECOND    PLANET    IN    THE    ORDER    OF  DIS- 
TANCE FROM  THE  SUN. 

THE  FIRST  PLANET  DISCOVERED.— MODE  OF  ITS  DISCOVERY.— HEB  ELONGATIONS. 
—MORNING  AND  EVENING  STAR.— A  SATELLITE  OF  THE  SUN.— HER  SUPERIOR 
AND  INFERIOR  CONJUNCTIONS. — HER  STATIONS. — DIRECT  AND  EETROGRADB 
MOTIONS. — THESE  PHENOMENA  INDICATE  A  MOTION  OF  THE  EARTH. — TRANSITS 
OF  VENUS. — INCLINATION  OF  THE  ORBIT  OF  VENUS  TO  THE  ECLIPTIC. — HER 
NODES. — INTEUVALS  OF  HER  TRANSITS. — KNOWLEDGE  OF  THE  ANCIENTS. — 
PHASES  OF  VENUS.— HER  ELONGATIONS  UNEQUAL.— No  SATELLITE  YET  DIS- 
COVERED.—SUN'S  LIGHT  AND  HEAT  AT  VENUS.— HER  ATMOSPHERE. 

THIS  planet  is  the  second  in  order  of  distance  from 
the  sun.  and  as  it  is  the  most  brilliant  of  all  the  orbs, 
with  the  exception  of  the  sun  and  moon,  it  was  undoubt- 
edly the  first  discovered  of  all  the  planets.  The  move- 
ments of  the  sun  and  moon  among  the  fixed  stars  must 
have  claimed  the  attention  of  the  observers  of  celestial 
phenomena  in  the  earliest  ages  of  the  world.  In  marking 
the  rising  and  setting  sun,  and  in  noting  the  stars  which 
were  the  last  to  fade  out  in  the  morning  twilight  and 
the  first  to  appear  in  the  evening  after  the  setting  of  the 
sun,  the  brilliancy  of  Venus  could  not  fail  to  have  at- 
tracted the  attention  of  the  very  first  observer  of  celestial 
phenomena.  A  star  of  unusual  brightness  was  noticed 
in  comparative  proximity  to  the  sun  in  the  early  evening. 
The  sun's  place,  with  reference  to  this  object,  having 
been  carefully  marked,  for  a  few  consecutive  nights,  it 
was  found  that  the  distance  between  them  was  rapidly 
diminishing.  It  was  readily  seen  that  this  diminution  of 


VENUS.  53 

distance  was  due  to  the  fact  that  the  bright  star  was  ap- 
proaching the  sun,  for  by  comparing  its  place  among  the 
fixed  stars  with  what  it  was  a  few  nights  previous,  this 
star  was  found  to  have  changed  its  position  among  the 
group  in  which  it  happened  to  be  located,  and  was  evi- 
dently advancing  rapidly  toward  the  sun. 

We  are  thus  presented  with  the  exact  facts  which  must 
have  marked  the  discovery  of  the  first  planet  or  wander- 
ing star  ever  revealed  to  the  eye  of  man.  \Ve  know  not 
the  name  of  the  discoverer,  nor  the  age  or  nation  to 
which  he  belonged,  but  we  are  satisfied  that  the  facts  as 
above  stated  did  undoubtedly  occur ;  and  we  find  not  only 
profane  authors  but  one  of  the  Hebrew  prophets  referring 
to  this  planet  more  than  two  thousand  five  hundred  years 
ago.  The  student  who  desires  may  easily  re-discover  the 
planet  Venus.*  She  will  be  readily  recognized  as  the 
largest  and  brightest  of  all  the  stars,  and  will  be  found 
never  to  recede  from  the  sun  more  than  about  47°.  From 
this  distance,  which  she  reaches  at  her  greatest  elonga- 
tion, the  planet  will  be  found,  at  first  slowly,  but  after- 
ward more  rapidly,  to  approach  the  solar  orb.  She  will 
finally  be  lost  in  the  superior  effulgence  of  the  sun ;  and 
when  the  unaided  eye  ceases  to  follow  her  in  her  approach 
to  the  sun,  telescopic  power  -will  enable  the  observer  to 
continue  his  observations  until,  finally,  the  sun's  direct 
beams,  mingling  with  those  of  the  planet,  she  ceases  to 
be  visible,  and  is  now  lost  for  a  greater  or  less  period, 
until  she  emerges  from  the  solar  rays,  appearing  just  be- 
fore the  sun  in  the  gray  morning  twilight.  She  now 
recedes  from  her  central  orb,  finally  reaches  her  greatest 
elongation  upon  the  opposite  side,  stops  in  her  career, 
returns  again,  and  thus  oscillates  backward  and  forward, 
never  passing  certain  prescribed  limits. 


61  VENUS. 

As  already  stated,  the  fact  that  Venus  was  a  planet  or 
wandering  star  must  have  become  known  among  the  very 
first  of  astronomical  discoveries ;  but  it  required,  doubt- 
less, a  long  series  of  observations  to  determine  the  truth 
that  the  bright  star,  which  for  some  months  had  accom- 
panied the  setting  sun,  and  which  was  at  length  lost  in 
the  solar  beams,  was  the  same  object  which,  at  a  later 
period,  became  visible  in  the  morning  dawn,  having  passed 
by  or  across  the  solar  disk.  This  discovery,  however,  M 
said  to  have  been  made  by  the  Egyptian  priests,  and  was 
by  them  communicated  to  the  Greek  astronomer,  Pytha- 
goras, who  taught  this  truth  to  his  countrymen. 

It  is  obvious,  from  the  above  facts,  that  the  planet 
Venus,  like  Mercury,  is  beyond  doubt  a  true  satellite  of 
the  sun,  even  to  the  inhabitants  of  the  earth,  and  it  is 
equally  manifest  that,  whatever  be  the  true  relations  be- 
tween the  earth  and  the  sun,  and  whichever  one  of  these 
two  bodies  may  be  at  rest,  one  thirig  is  certain,  the  planets 
Mercury  and  Venus  cannot  by  any  possibility  have  the 
earth  for  their  center  of  motion.  No  matter  in  what 
region  of  the  heavens  the  sun  may  be  found  at  any  season 
of  the  year,  these  two  inferior  planets  ever  accompany 
him.  As  Venus  recedes  to  a  greater  distance  from  the 
sun  than  Mercury,  it  follows  that  her  orbit  of  revolution 
around  the  sun  must  be  the  larger  of  the  two.  We  are 
thus  enabled,  by  the  simplest  train  of  reason  and  obser- 
vation, to  fix  the  following  facts  : — The  sun  is  a  central 
orb,  about  which  revolve,  in  regular  order,  two  planets, 
the  nearest  of  which  is  Mercury,  and  next  to  Mercury, 
Venus,  with  periods  of  revolution,  readily  determined  by 
the  spectator  on  the  earth's  surface.  These  facts  are  ex- 
ceedingly important  as  the  primary  ones  which  lead  to 
the  discovery  of  the  true  system  of  the  universe. 


VENUS.  55 

When  Venus  passes  between  the  eye  of  the  observer 
and  the  sun,  she  is  said  to  be  in  her  inferior  conjunc- 
tion; when  she  is  directly  beyond  the  sun,  with  reference 
to  the  spectator,  she  is  in  her  superior  conjunction. 
From  her  inferior  to  her  superior  conjunction  she  occu- 
pies a  position  west  of  the  sun,  rises  in  the  early  morning, 
before  the  sun,  and  is  known  as  Phosphorous,  or  Lucifer, 
or  the  morning  star.  From  her  superior  to  her  inferior 
conjunction  she  follows  the  setting  sun ;  she  becomes 
our  evening  star,  under  the  name  of  Hesperus. 

In  examining  the  phenomena  involved  in  the  motions 
of  Venus,  and  watching  her  carefully  in  her  approach  to, 
and  in  her  recess  from  the  sun,  it  is  found  that  her  move- 
ments are  almost  identical  with  those  of  Mercury — her 
motions  for  a  certain  portion  of  her  revolution  being 
direct,  or  like  those  of  the  sun ;  she  then  becomes  sta- 
tionary, then  moves  backward  or  retrograde  among  the 
fixed  stars,  becomes  stationary  again,  and  then  com- 
mences her  direct  movement.  All  these  facts  are  readily 
accounted  for  by  admitting  that  Venus  revolves  about 
the  sun  in  an  orbit  nearly  circular,  and  that  she  is  viewed 
by  a  spectator  situated  exterior  to  her  orbit,  and  moving 
around  the  sun  and  Venus  in  a  circle,  wRse  plane  makes 
a  small  angle  with  the  plane  on  which  fie  orbit  of  Venus 
lies.  If  a  visual  ray  be  drawn  from  the  eye  of  the  observ- 
er, tangent  to  the  orbit  of  Venus,  should  the  planet  hap- 
pen to  fill  the  point  of  contact,  she  will  appear  to  move 
in  the  direction  of  this  ray,  and,  for  the  time  being,  will 
be  directly  advancing  to,  or  receding  from,  the  eye  of  the 
observer,  and  thus  will  appear  stationary.  That  the  ob- 
server is  in  motion,  is  manifest  from  the  fact  that  the 
direct  movement  of  Venus  does  not  bear  that  relation  to 
the  retrograde  movement  which  is  required  by  such  an 


56  VENUS. 

hypothesis.  Indeed,  if  two  visual  rays  were  drawn  from 
the  eye  of  a  stationary  observer,  tangent  to  the  orbit  of 
Venus,  she  would  appear  to  move  from  one  point  of  con- 
tact to  the  other,  on  the  hither  side  of  her  orbit,  with  a 
direct  motion,  while  on  the  further  side  of  her  orbit,  be- 
tween the  points  of  contact,  her  motion  would  appear 
retrograde.  These  facts,  however,  are  not  presented  in 
nature,  and  would  be  subverted,  of  course,  by  supposing 
the  spectator  to  be  in  motion.  In  case  the  spectator  were 
to  occupy  the  line  passing  from  the  sun's  centre  through 
Venus,  and  to  revolve  about  the  sun  in  the  same  period 
occupied  by  the  planet,  then  would  the  planet  always  be 
seen  in  inferior  conjunction  with  the  sun.  As  this  is  not 
the  fact  in  observation,  it  is  manifest  that  the  angular 
velocity  of  the  spectator  is  not  so  great  as  that  of  the 
planet  Venus,  as  she  finally  emerges  from  the  sun's  rays, 
after  her  inferior  conjunction,  beyond  the  line,  joining 
the  sun's  center  and  the  eye  of  the  beholder.  Here,  then, 
is  another  important  fact,  which  must  be  taken  into  ac- 
count when  we  shall  inquire  into  the  true  system  of  na- 
ture, as  presented  in  the  organization  of  the  planetary 
worlds. 

In  case  the  eye  of  the  observer  were  located  in  the 
same  plane  in  which  the  orbit  of  Venus  lies,  this  plane, 
passing,  as  it  does,  through  the  sun's  center,  it  is  clear 
that  at  every  inferior  conjunction  of  the  planet  there 
might  be  seen  a  transit  of  Venus,  while  at  every  su- 
perior conjunction,  the  planet  would  be  occulted,  or  hid- 
den, by  passing  actually  behind  the  disk  of  the  sun.  It 
happens,  however,  that  the  plane  of  the  orbit  of  Venus 
does  not  coincide  with  the  plane  of  the  ecliptic,  or  earth's 
orbit.  These  planes  are  inclined  to  each  other,  under  an 
angle  of  3°  23'  28".5,  one  half  of  the  orbit  of  Venus 


VENUS.  57 

lying  above,  or  north  of  the  ecliptic,  the  other  half  lying 
below,  or  south  of  the  ecliptic.  The  point  in  which 
Venus  passes  from  the  north  to  the  south  side  of  the 
ecliptic  is  called  the  descending  node.  She  returns  from 
the  south  to  the  north  of  this  plane  through  the  ascend- 
ing node,  and  the  line  joining  these  two  points  is  called 
the  line  of  nodes. 

The  transits  of  Venus,  unfortunately  for  astronomical 
science,  are  of  very  rare  occurrence,  and  are  separated 
by  intervals  of  time  which  are  very  un^Hl.  The  peri 
ods  from  transit  to  transit  are  8,122,  8,^,  8,122,  &c., 
years,  for  a  long  period  falling  in  the  months  of  June  and 
December.  As  already  stated,  no  transit  can  occur  ex- 
cept when  the  planet  is  in  the  act  of  passing  her  node  at 
her  inferior  conjunction,  while,  at  the  same  time,  the 
earth  is  crossing  the  line  of  nodes  of  the  planet  prolonged. 
This  line  of  nodes,  though  not  fixed,  moves  very  slowly, 
and  at  this  time  crosses  the  earth's  "orbit  in  those  re- 
gions passed  over  by  the  earth  in  the  months  of  June 
and  December.  After  a  transit  the  relative  motion  of 
Venus,  the  earth,  and  the  node  of  the  orbit  of  Venus,  is 
such  as  to  render  it  certain  that  within  eight  years  an- 
other transit  will  occur,  as  within  this  period  Venus  does 
not,  at  her  inferior  conjunction,  recede  too  far  from  the 
plane  of  the  ecliptic  to  render  her  transit  impossible. 

In  our  account  of  the  determination  of  the  solar  paral- 
lax (Chap.  I)  we  have  stated  that  the  distance  of  Venus 
is  readily  determined  by  the  measure  of  her  horizontal 
parallax.  Her  distance  may  also  be  determined,  after  we 
have  learned  the  distance  of  the  sun,  by  the  same  method 
used  in  measuring  the  distance  of  Mercury  (Chap.  II). 

By  these  and  other  methods  the  mean  distance  of  this 
planet  from  the  sun  is  found  to  be  about  sixty-eight 


58  VENUS. 

millions  of  miles,  and  from  the  measure  of  her  apparent 
diameter  we  conclude  her  actual  diameter  to  be  7,700 
miles,  or  a  little  less  than  the  diameter  of  the  earth,  as 
we  shall  see  hereafter. 

The  period  of  rotation  of  Venus  has  not  been  well  de- 
termined, but  from  an  examination  of  indistinct  spots, 
sometimes  visible  on  her  face,  it  is  conjectured  that  she 
rotates  on  her  axis  in  about  twenty-four  hours,  or  in  the 
same  period  occupied  by  the  earth. 

The  chang4fcn  the  brilliancy  of  the  planet  Venus 
are  accounte^ior  in  a  two -fold  way.  In  case  the 
observer  is  really  exterior  to  her  orbit,  as  the  planet's 
distance  from  the  sun  is  on  the  average  68,000,000 
of  miles,  then  when  the  planet  occupies  that  point  in 
her  orbit  nearest  the  observer  she  will  be  closer  to  the 
eye  than  when  in  the  opposite  point  of  her  orbit  by  an 
amount  equal  to  no  less  than  double  her  mean  dis- 
tance from  the  sun,  or  136,000,000  of  miles.  We  readily 
perceive  that  this  vast  increase  of  distance  must  diminish 
in  direct  proportion  the  apparent  diameter  of  the  planet, 
and  thus  her  brightness  must  decline,  as  she  recedes  from 
her  nearest  to  her  greatest  distance  from  the  observer. 
To  this  cause,  however,  of  a  change  of  brilliancy,  is  to  be 
added  another  of  still  greater  importance.  We  have 
already  stated  that  the  planet  Venus,  when  seen  pro- 
jected upon  the  sun's  disk  during  her  transit,  ap- 
pears as  a  round,  black  spot  on  the  brilliant  surface 
of  the  sun.  This  fact  demonstrates,  beyond  a  doubt, 
that  the  planet  Venus  is  a  dark,  opaque  globe,  destitute 
of  light,  and  only  visible  by  reflecting  the  light  which  it 
receives  from  the  sun.  If  further  evidence  of  this  state- 
ment were  wanting,  it  is  found  in  the  fact  that  after  the 
planet  passes  her  inferior  conjunction  and  becomes  visi- 


PHASES  OF  VENUS 


VENUS.  59 

ble  in  emerging  from  the  sun's  beams,  she  is  first  seen 
by  the  telescope  as  a  slender  and  delicate  crescent  of 
silver  light.  As  she  recedes  from  the  sun  this  phase 
gradually  changes;  more  and  more  of  her  illuminated 
hemisphere  becomes  visible,  until,  finally,  at  her  superior 
conjunction,  her  disk  becomes  round  and  well-defined. 
The  same  facts  are  true  of  the  planet  Mercury,  and  thus 
is  added  another  powerful  evidence  that  these  two  planets 
are  satellites  of  the  sun,  revolving  about  this  luminary  in 
orbits  nearly  circular,  and  deriving  their  light  from  this 
great  central  body. 

When  we  come  to  measure  accurately  the  greatest 
elongations  of  Venus  we  find  them  unequal.  In  case 
the  spectator  were  stationary,  and  admitting  the  circular 
form  of  the  orbit  of  Venus,  these  inequalities  could  not 
occur.  We  thus  are  led  to  believe,  either  that  the  orbit 
of  the  planet  is  not  circular,  or,  if  it  be  circular,  that  the 
sun  is  eccentrically  situated,  or  that  the  observer  himself 
is  in  motion. 

It  is  possible  that  any  two,  or  even  all  of  these  causes, 
may  combine  to  produce  the  phenomena  presented  in  the 
movements  of  Venus.  We  shall  recur  again  to  these 
matters  when  we  come  to  consider  the  great  problem  of 
the  true  system  of  the  universe. 

The  extreme  brightness  of  this  planet  makes  it  a  very 
beautiful  but  difficult  object  for  telescopic  observation. 
Although  spots  have  been  seen  upon  the  surface  of 
Venus,  and  by  their  close  examination  her  period  of  ro- 
tation upon  her  axis  has  been  approximately  determined, 
I  have  never  been  able,  at  any  time,  with  the  powerful 
refractor  of  the  Cincinnati  Observatory,  to  mark  any 
well-defined  differences  in  the  illumination  of  her  sur- 
face. If  we  are  to  trust  to  the  observations  of  others, 


60  VENUS. 

the  inequalities  which  diversify  the  planet  Venus  far  ex- 
ceed in  grandeur  those  found  upon  our  earth.  It  is 
stated  by  Mr.  Schroter  that,  from  his  own  observations, 
the  mountains  of  Venus  reach  an  altitude  five  or  six 
times  greater  than  the  loftiest  mountains  of  our  own 
globe. 

It  has  been  affirmed  by  several  distinguished  as- 
tronomers that  this  planet  is  accompanied  by  a  minute 
satellite,  but  by  the  application  of  the  most  powerful 
telescopes,  during  the  present  century,  and  after  the 
most  rigid  examination,  this  statement  has  not  been  con- 
firmed. It  was  supposed  that  during  the  transit  which 
occurred  in  1769  the  disputed  question  as  to  the  ex- 
istence of  a  moon  of  Venus  would  be  positively  settled. 
While  the  planet  was  distinctly  seen  as  a  dark  spot 
upon  the  surface  of  the  sun,  no  telescopic  power  could 
detect  any  dark  object  which  might  be  a  satellite.  Al- 
though we  cannot  absolutely  affirm  that  Venus  has  no 
satellite,  we  may  safely  say,  that  -  if  there  be  one  it  yet 
remains  to  be  discovered. 

The  amount  of  light  and  heat  which  the  earth  would 
receive  from  the  sun,  if  revolving  in  the  orbit  of  Venus, 
would  be  nearly  twice  as  great  as  that  now  received  ;  but 
this  does  not  justify  us  in  concluding  that  the  planet 
Venus  has  a  mean  temperature  nearly  double  that  of  the 
earth.  We  know  that  a  powerful  influence  is  exerted  by 
the  earth's  atmosphere  to  modify  the  solar  heat.  There 
may  exist  an  atmosphere  surrounding  Venus  such  that 
the  temperature  at  her  surface  may  be  no  greater  than 
our  own.  It  is  useless,  however,  as  we  have  already  re- 
'marked,  for  us  to  speculate  about  matters  concerning 
which  we  positively  know  nothing.  There  are  some  in- 
dications in  the  telescopic  appearance  of  Venus  that  she 


VENUS:  61 

is  surrounded  by  an  extended  atmosphere.  When  pre- 
senting the  form  of  a  crescent  of  light,  the  slender  horns 
are  found  sometimes  to  extend  beyond  the  limits  of  a 
semi-circumference — a  fact  only  to  be  accounted  fci",  BO 
far  as  we  know,  by  admitting  atmospheric  refraction. 


CHAPTER    IV. 


THE    EAKTH    AND   ITS  SATELLITE:    THE    THIRD   PLANET 
IN   THE    ORDER   OF   DISTANCE   FROM   THE   SUN. 

TUB  EAKTH  THE  APPARENT  CENTER  OF  MOTION.— To  ALL  THE  SENSES  IT  is  AT 
EEST. — THE  CENTER  OF  THE  MOTIONS  OF  THE  SUN  AND  MOON. — EXPLANATION 
OF  THE  ACCELERATION  OF  THE  ORBITUAL  MOTION  OF  THE  SUN  AND  MOON. — 
PTOLEMY'S  EPICYCLES. — THE  EXPLANATION  OF  COPERNICUS. — THE  SUN  THK 
CENTER  OF  PLANETARY  MOTION. — THE  EARTH  ONE  OF  THE  PLANETS. — OB- 
JECTIONS TO  THIS  HYPOTHESIS.— THE  ANSWER. — SYSTEM  or  JUPITER  DISCOV- 
ERED BY  THE  TELESCOPE. — THE  OLD  SYSTEM  SUPERSEDED  BY  THE  NEW. — THE 
FIGURE  AND  MAGNITUDE  OF  THE  EARTH.— How  DETERMINED. — THE  EARTH'S 
MOTIONS. — ROTATION  AND  REVOLUTION. — A  UNIT  OF  TIME  FURNISHED  BY 
THE  EARTH'S  PERIOD  OF  ROTATION. — EARTH'S  ORBITUAL  MOTION. — VERNAL 
EQUINOX. — PERIHELION  OF  EARTH'S  ORBIT. — ITS  PERIOD  OF  REVOLUTION. — 
SOLAR  AND  SIDEREAL  TIME. 

THE  MOON.— REVOLUTION  IN  HER  ORBIT.— HER  PHASES.— EARTH'S  LINE.— EC- 
CENTRICITY OF  HER  ORBIT.— REVOLUTION  OF  HER  APOGEE.— INCLINATION  OP 
HER  ORBIT.— MOON'S  PARALLAX  AND  DISTANCE.— HER  PHYSICAL  CONSTITIT 
TION. — CENTER  OF  GRAVITY  AND  CENTER  OF  FIGURE. 

THE  ancients  did  not  reckon  the  earth  as  one  of  the 
planetary  orbs.  There  seemed  to  be  no  analogy  between 
the  world  which  we  inhabit,  with  its  dark,  opaque,  arid 
diversified  surface,  and  those  brilliant  planets  which  pur- 
sued their  mysterious  journey  among  the  stars.  Sunk 
as  they  were,  so  deep  in  space,  it  was  very  difficult  to 
reach  any  correct  knowledge  of  their  absolute  magnitude. 
The  earth  seemed,  to  the  senses  of  man,  vastly  larger 
than  any  or  all  of  these  revolving  worlds.  About  the 
earth,  as  a  fixed  center,  the  whole  concave  of  the  heavens, 
with  all  its  starry  constellations,  appeared  to  revolve, 
producing  the  alternations  of  day  and  night.  It  was  not 
unnatural,  therefore,  knowing  the  central  position  of  the 


THEEARTH.  63 

earth  with  reference  to  the  fixed  stars,  to  assume  its  cen- 
tral position  with  reference  to  the  sun,  and  moon,  and 
planetary  worlds. 

There  is  no  problem  perhaps  so  difficult  as  that  pre- 
sented in  the  attempt  to  discriminate  between  real  and 
apparent  motion.  To  all  the  senses  the  earth  appeared 
to  be  absolutely  at  rest.  It  could  not  be  affirmed  that 
any  one  had  ever  seen  it  move,  or  felt  it  move,  or  heard 
it  move,  while  the  sense  of  sight  bore  the  most  positive 
testimony  to  the  motion  of  the  surrounding  orbs.  It  must 
be  remembered  that,  in  the  primitive  ages,  the  great 
objects  of  observation  and  study  were  the  sun  and  moon. 
Five  planets  were  indeed  discovered,  at  a  period  so  re- 
mote that  no  historic  record  of  the  facts  of  their  discovery 
now  exists.  They  seem  to  have  been  known  to  all  the 
nations  of  antiquity,  and  a  knowledge  of  their  existence 
appears  to  have  been  derived  from  a  common  origin,  as 
we  shall  have  occasion  to  notice  more  particularly  here- 
after. A  few  of  the  more  obvious  phenomena  presented 
in  the  planetary  movements  were  known  and  studied  by 
the  old  astronomers,  but  when  these  motions  became  to 
them  inexplicable,  they  frankly  confessed  that  these 
matters  must  be  left  for  the  study  and  development  of 
posterity. 

If,  then,  we  confine"  our  attention  principally  to  an 
examination  of  the  solar  and  lunar  motions,  and  to  the 
general  revolution  of  the  sphere  of  the  fixed  stars,  in  our 
efforts  to  determine  the  true  position  and  condition  of  the 
earth,  we  shall  find  ourselves  compelled,  as  were  the 
celebrated  Greek  astronomers,  Hipparchus  and  Ptolemy, 
to  admit  not  only  the  earth's  central  position  but  also  its 
absolute  immobility.  It  is,  undoubtedly,  central  to  the 
moon's  motions,  and  it  is  equally  central  to  the  sun's 


64  THE     EARTH. 

movement ;  that  is  to  say,  all  the  phenomena  of  the  solar 
motions  are  as  well  accounted  for  by  supposing  the  earth 
to  be  the  center  about  which  the  sun  revolves,  as  by  sup- 
posing the  converse  hypothesis,  that  the  sun  is  the  center 
about  which  the  earth  revolves. 

So  far,  then,  as  these  two  great  luminaries  are  con- 
cerned, the  hypothesis  of  the  earth's  central  position  is 
well  sustained,  and  almost  indisputable.  It  is  only  when 
we  extend  our  investigations  to  the  inferior  and  superior 
planets,  and  gather  together  a  multitude  of  facts  and 
phenomena  demanding  explanation,  that  we  find  ourselves 
necessarily  driven  into  so  great  complexity  by  retaining 
the  central  position  of  the  earth,  that  at  last  we  begin  to 
doubt.  We  have  already  noticed  the  remarkable  move- 
ments of  the  two  planets  Venus  and  Mercury.  We  shall 
find  hereafter  that  phenomena  of  a  like  character  were 
presented  in  the  movements  of  Mars,  Jupiter,  and  Sa- 
turn, each  of  which  planets  was  distinguished  by  its  sta- 
tions, retrogradations,  and  advances  among  the  fixed 
stars.  The  ancients  not  only  adopted  the  hypothesis  of 
the  earth's  central  position  and  immobility,  but,  for  evi- 
dent reasons,  likewise  adopted  the  hypothesis  that  all  mo- 
tion was  performed  in  circular  orbits,  and  with  uniform 
velocity.  We  have  already  seen,  in  our  examination  of 
the  solar  motions,  that  this  orb  did  not  move  to  the  eye 
with  uniform  velocity,  but  this  apparent  deviation  from 
uniformity  was  readily  accounted  for  by  supposing  the 
earth  to  be  placed  a  little  eccentric  with  reference  to  the 
sun's  circular  orbit.  The  same  facts  becoming  known 
with  reference  to  the  moon's  motion,  a  like  hypothesis 
was  adopted,  and  the  earth  was  placed  eccentrically  within 
the  lunar  orbit.  In  marking  the  planetary  movements, 
they  were  found,  however,  to  difier  radically  in  some 


THEEAETH.  65 

particulars  from  the  movements  of  the  sun  and  moon. 
While  these  great  luminaries  always  advanced  in  their 
revolution  among  the  fixed  stars,  the  planets  were  found, 
in  making  their  revolution,  not  only  to  stop,  but  for  a 
time  actually  to  turn  back,  then  stop  again,  and  finally 
to  resume  their  onward  movement.  No  eccentric  posi- 
tion of  the  earth  could  account  for  these  stations  and  retro- 
gradations  ;  but  a  very  simple  expedient  was  devised, 
which  rendered  a  satisfactory  account,  in  the  primitive 
astronomical  ages,  of  these  curious  phenomena.  Retain- 
ing the  central  position  of  the  earth  and  the  circular 
figure  of  the  planetary  orbits,  each  planet  was  supposed 
to  revolve  on  the  circumference  of  a  small  circle^  whose 
center  was  carried  uniformly  around  on  the  circumfer- 
ence of  the  great  circle  constituting  the  orbit  of  the 
planet.  By  such  machinery  it  will  be  seen  that  it  be- 
came possible  to  render  a  satisfactory  account  of  the  sta- 
tions and  retrogradations  of  the  planets,  for  while  the 
planet  was  describing  that  portion  of  the  small  circle  in 
which  it  revolved,  nearest  to  the  eye  of  the  spectator,  it 
would  seem  to  move  backward  in  the  order  of  the  fixed 
stars.  Again,  in  coming  directly  toward  the  eye  of  the 
spectator,  or  in  moving  in  the  opposite  direction  along 
two  visual  rays,  drawn  tangent  to  its  small  circle,  the 
planet  would  appear  stationary.  Such  was  the  general 
exposition  of  the  Greek  astronomer  Hipparchus,  whose 
theory  was  enlarged  and  extended  by  his  successor 
Ptolemy,  whose  theory  of  astronomy,  based  upon  the 
central  position  of  the  earth,  known  as  the  Ptolemaic 
System,  endured  for  more  than  fifteen  hundred  years. 
It  was  only  after  a  long  lapse  of  time,  and  by  the  dis- 
covery of  a  large  number  of  irregularities  in  the  solar, 
lunar,  and  planetary  motions,  making  it  necessary  (to 


66  THE     EARTH. 

render  a  just  account  of  them)  to  increase  the  number  of 
these  small  circles,  which  were  called  epicycles,  that 
the  whole  scheme  finally  became  so  cumbrous  and  com- 
plicated that,  after  long  and  laborious  study,  extending 
through  more  than  thirty  years  of  diligent  observation, 
the  great  Polish  astronomer,  Copernicus,  found  himself 
compelled  to  abandon  the  old  hypothesis  of  the  central 
position  of  the  earth,  and  to  attempt  a  new  solution  of  the 
great  problem  of  the  universe. 

In  giving  up  the  earth  as  the  centre  about  which  the 
worlds  were  revolving,  there  was  little  difficulty  in  se- 
lecting the  object  which,  in  greatest  probability,  occupied 
the  true  center.  All  the  movements  of  the  sun  could, 
without  the  slightest  difficulty,  be  transferred  to  the 
earth,  and  thus,  the  sun  could  become  central  to  the 
earth,  revolving  as  one  among  the  planets.  This  hypo- 
thesis did  not  require  any  change  whatever  in  the  com- 
putation of  those  tables  which  gave  from  day  to  day  the 
sun's  apparent  place  among  the  fixed  stars.  Again,  as 
we  have  already  seen,  the  planets  Mercury  and  Venus 
were  undoubtedly  satellites  of  the  sun,  whether  the  Sun 
be  at  rest  or  in  motion ;  and  with  these  suggestions,  the 
vigorous  mind  of  Copernicus,  transferring  himself,  in 
imagination,  to  the  sun,  and  thence  looking  out  upon  the 
planetary  revolutions,  found  that  a  large  number  of  those 
complexities  and  irregularities  which  had  so  confounded 
him  when  viewed  from  the  earth's  surface  were  swept 
away  for  ever.  When  seen  from  the  sun,  as  the  center 
of  motion,  all  the  stations  and  retrbgradations  in  the 
planetary  revolutions  disappeared.  The  complications  in 
the  movements  of  Mercury  and  Venus  were  reduced  to 
perfect  order  and  simplicity  when  seen  from  the  sun. 
The  earth  itself  assumed  its  proper  rank  among  the 


THE     E  A  B  T  H  .  67 

planetary  worlds,  dignified  by  the  attendance  of  its  satel- 
lite the  moon,  and  beyond  the  earth,  the  planets  Mars. 
Jupiter,  and  Saturn,  performed  their  orderly  revolution 
in  orbits  nearly  circular.  Such  is  the  true  scheme  of 
nature  in  its  grand  outlines,  as  given  to  the  world  by 
Copernicus.  It  will  be  seen  that  one  of  the  remarkable 
features  of  the  old  system,  namely,  the  uniform  circular 
movement  of  the  planets,  was  retained  by  the  Polish  as- 
tronomer. By  the  use  of  eccentrics  and  epicycles,  Co- 
pernicus found  it  possible  to  render  a  satisfactory  account 
of  all  the  phenomena  of  the  solar  system  known  during 
his  age.  We  can  readily  comprehend  that  a  system  in- 
volving the  startling  doctrine  of  the  swift  rotation  of  the 
earth  upon  its  axis,  and  the  rapid  flight  of  its  entire 
mass,  with  all  its  continents,  and  oceans,  and  mountains, 
through  space,  must  have  been  received  by  the  human 
mind  with  the  greatest  distrust.  Indeed,  there  seemed 
to  be  to  the  eye  positive  proof  that  this  bold  theory  was 
absolutely  false.  It  was  urged  by  the  anti-Copernicans, 
that  in  case  the  earth  did  revolve  about  the  sun  in  an 
orbit  of  nearly  two  hundred  millions  of  miles  in  diame- 
ter, that  the  point  where  the  axis  of  rotation,  prolonged 
to  the  sphere  of  the  fixed  stars,  pierced  the  heavens,  must 
by  necessity  travel  around  and  describe  a  curve  among 
the  stars  identical  with  that  described  by  the  earth  in  re- 
volvino-  about  the  sun.  Now.  as  no  such  motion  of  the 

O  ' 

north  polar  point  was  visible  to  the  eye,  but  as  the  axis 
of  the  heavens  remained  for  ever  fixed  among  the  stars, 
it  proved  beyond  dispute  the  absolute  impossibility  of  the 
earth's  revolution  about  the  sun.  This  train  of  reason- 
ing was  undeniably  true,  and  the  only  response  which 
the  Copernicans  could  make  was  this  :  "  The  earth  does 
revolve  about  the  sun ;  the  earth's  axis  prolonged  does 


68  THE     EARTH.  ... 

pierce  the  celestial  concave  in  successive  points,  describ- 
ing a  curve  precisely  like  the  earth's  orbit,  and  whose  diam- 
eter is  indeed  nearly  200,000,000  of  miles  ;  but  that  the 
distance  of  the  fixed  stars  is  so  great,  that  an  object  hav- 
ing this  immense  diameter  actually  shrinks  into  an  in- 
visible point,  on  account  of  the  almost  infinite  distance  to 
which  it  is  removed  from  the  eye  "of  the  beholder;"  and 
with  this  answer  the  world  was  compelled  to  rest  satisfied 
for  more  than  two  hundred  years. 

The  doctrines  of  Copernicus  gained  a  great  accession 
of  strength  by  the  invention  of  the  telescope.  By  the 
use  of  this  extraordinary  instrument  not  only  were  the 
phases  of  Mercury  and  Venus  detected,  but  also  the 
greater  discovery  of  the  satellites  of  Jupiter,  presenting, 
in  this  central  orb,  with  his  four  revolving  moons,  a,  sort 
of  miniature  likeness  of  the  grander  system,  having  the 
sun  for  its  center.  The  simplicity  of  the  hypothesis  pre- 
sented in  the  Copernican  system,  the  numerous  compli- 
cations which  it  removed  from  the  heavens,  and  the  satis- 
factory account  which  it  yielded  of  the  discoveries  made 
by  the  telescope,  caused  it  to  be  adopted  'and  defended 
by  some  of  the  best  minds  of  the  age  immediately  follow- 
ing that  of  Copernicus,  among  whom  none  is  more  dis- 
tinguished than  the  great  Florentine  astronomer  and 
philosopher  Galileo  Galillei.  It  is  hardly  necessary  to 
mention  the  historical  fact,  that  the  old  system  of  astron- 
omy, which  had  held  its  sway  over  the  human  mind  for 
more  than  2,000  years,  did  not  fall  without  a  severe 
struggle.  The  astronomy  of  Ptolemy,  and  the  philosophy 
of  Aristotle,  had  taken  so  deep  a  hold  of  mankind,  and 
were  so  firmly  interwoven  with  all  the  systems  of  educa- 
tion and  of  science,  that  we  must  behold  with  astonish- 
ment the  downfall  of  systems  venerable  from  their  an- 


THEEAETH.  69 

tiquity,  and  whose  ruin  could  only  be  accomplished  by 
the  desertion  of  their  adherents. 

THE    FIGURE    AND    MAGNITUDE   OF   THE    EARTH. — A 

knowledge  of  the  globular  figure  of  the  earth  seems  to 
have  been  reached  at  an  early  period  in  the  history  of 
astronomy.  Indeed,  the  concave  heavens,  presenting  to 
the  eye  a  hemisphere  above  the  horizon,  and,  undoubtedly, 
extending  beneath  the  earth,  so  as  to  complete  the  grand 
hollow  sphere,  suggested  at  once  that  the  inclosed  earth, 
minute  in  its  dimensions  when  compared  with  the  celes- 
tial globe  by  which  it  was  encompassed,  might  also  have 
the  globular  form.  The  curvature  of  the  earth's  surface 
becomes  at  once  visible  to  the  eye  in  marking  the  gradual 
approach  of  a  ship  at  sea.  At  first  only  the  top  of  the 
mast  can  be  discovered,  even  with  a  glass,  all  the  remain- 
ing parts  of  the  vessel  being  hidden  by  the  outline  of  the 
the  interposed  water.  As  the  distance  diminishes,  more 
and  more  of  the  ship  lifts  itself  above  the  horizon,  until, 
finally,  the  water-line  comes  into  sight.  The  same  evi- 
dence of  the  rotundity  of  the  earth  is  furnished  by  the 
circular  form  of  the  horizon  which  always  sweeps  round 
a  beholder  who  ascends  to  the  summit  of  a  lofty  moun- 
tain. Thus,  we  are  disposed  to  adopt  the  spherical  form 
of  the  earth  in  consequence  of  its  simplicity,  even  before 
we  have  any  conclusive  demonstration  as  to  its  real  form. 

The  Greek  astronomers  comprehended  the  simple  pro- 
cess, whereby  not  only  the  true  figure  of  the  earth  might 
be  obtained,  but  in  case  it  were  spherical,  whereby  its 
real  diameter  and  absolute  magnitude  might  be  deter- 
mined. 

This  process  is  remarkably  simple.  Suppose  an  ob- 
server, provided  with  the  means  of  directing  a  telescope 
precisely  to  the  zenith  of  any  given  station,  and  in  the 


TO  THE     EARTH. 

zenith  point  he  marks  a  star,  which  from  its  magnitude 
and  position  he  can  readily  find  again.  Now,  leaving 
this  first  station,  and  moving  due  north,  measuring  the 
distance  over  which  he  passes,  he  will  find  that,  as  he 
progresses  toward  the  north,  the  star  under  examination 
will  leave  the  zenith  and  slowly  decline  toward  the  south. 
Suppose  the  observer  to  halt,  set  up  his  instrument,  and 
find  that  his  star  has  declined  one  degree  from  the  zenith 
toward  the  south. 

This  demonstrates  that  he  has  traveled  from  the  first 
station  to  the  second,  over  one  degree  of  a  great  circle  of 
the  earth,  or  one  part  in  360  of  the  entire  circumference 
of  the  earth.  It  follows  that,  in  case  the  earth  is  really 
globular  in  form,  the  distance  between  the  stations,  multi- 
plied by  360,  will  give  the  length  of  the  entire  circum- 
ference, and  this  quantity,  divided  by  3.14159  (the  ratio 
between  the  circumference  of  a  circle  and  its  diameter), 
will  give  the  value  of  the  earth's  diameter. 

It  is  by  methods  analogous  to  the  above  that  the  true 
figure  and  actual  magnitude  of  the  earth  have  been  de- 
termined. Very  numerous  and  delicate  measures,  per- 
formed in  many  parts  of  the  earth's  surface,  have  revealed 
the  surprising  fact  that  the  true  figure  of  the  earth 
is  not  that  of  a  sphere,  but  of  a  spheroid,  being  more 
flattened  at  the  poles  and  more  protuberant  at  the  equa- 
tor than  a  true  sphere.  We  shall  hereafter  exhibit  the 
cause  of  this  remarkable  fact,  and  present  some  very 
curious  and  surprising  results  and  phenomena  which 
flow  from  it.  By  the  most  reliable  measure  we  find  the 
polar  diameter  of  the  earth  to  be  7,898  miles,  while  the 
diameter  of  the  equator  reaches  to  7,924,  being  an  excess 
of  no  less  than  twenty-six  miles,  which  excess  would  have 
to  be  trimmed  off  to  reduce  the  earth  to  a  globular  form. 


THEEARTH.  71 

THE  EARTH'S  MOTION. — We  have  already  noticed  the 
fact  that  the  sun,  as  well  as  the  planets  thus  far  described, 
have  a  motion  of  rotation  about  a  fixed  axis,  while  the 
planets  have  also  a  motion  of  revolution  in  their  orbits. 
Since  we  are  compelled  to  recognize  the  earth  as  one  of 
the  planets,  we  naturally  conclude  that  it  will  be  dis- 
tinguished by  the  same  motions  which  mark  the  on- 
goings of  the  other  planets.  We  shall  find,  indeed,  that 
the  earth  has  three  motions :  a  motion  of  rotation  about 
an  axis,  accomplished  in  a  period  of  twenty- four  hours, 
and  producing  an  apparent  revolution  of  the  sphere  of 
the  fixed  stars  in  the  same  period.  A  motion  of  revolu- 
tion in  an  orbit  whereby  the  earth  is  carried  entirely 
around  the  sun,  effecting  all  those  changes  which  mark 
upon  the  earth's  surface  the  seasons  of  the  year,  and  pro- 
ducing at  the  same  time  an  apparent  revolution  of  the 
sun  in  a-  circular  orbit  among  the  fixed  stars.  The  earth 
has  a  third  motion,  (which  we  will  examine  more  fully 
hereafter,)  occasioned  by  the  fact  that  its  axis  of  rotation 
does  not  remain  constantly  parallel  to  itself. 

THE  EARTH'S  ROTATION. — Let  us  return  to  the  con- 
sideration of  the  diurnal  revolution,  to  the  inhabitants 
of  the  earth,  as  well  as  to  the  student  of  astronomy, 
by  far  the  most  important  motion  which  has  been  re- 
vealed by  human  investigation.  It  is,  perhaps,  impos- 
sible for  the  mind  of  man  to  form  any  just  notion  of 
what  we  call  time,  except  as  its  flow  is  measured  by 
some  absolutely  uniform  succession  of  events.  This  per- 
fect measure  of  time  is  found  in  the  uniform  rotation 
of  the  earth  upon  its  axis,  whereby  all  the  fixed  stars 
appear  to  the  eye  to  perform  revolutions  in  circles  of 
greater  or  less  diameter,  all  in  the  same  identical  period, 
and  with  a  motion  which,  so  far  as  we  know,  is  abso- 


72  THE     EARTH. 

lutely  uniform.  Thus  the  duration  of  one  rotation  of  the 
earth  upon  its  axis,  whereby  any  given  fixed  star  re- 
volves from  the  meridian  of  any  place  entirely  round  to 
the  same  meridian  again,  furnishes  to  man  a  unit  of 
time,  which,  by  its  sub-divisions  and  multiplications, 
renders  it  possible  to  take  account  of  historic  and  other 
events,  and  to  mark  their  relations  to  each  other,  not 
only  in  the  order  of  time,  but  also  in  the  interval  of  time. 
QMms,  a  day  is  sub-divided  into  hours,  minutes  and 
seconds-,  and  the  fraction  of  a  second,  and  by  successive 
additions  gives  us  larger  portions  of  time,  as  weeks, 
months,  years,  and  centuries.  To  serve  this  very  im- 
portant purpose,  and  to  become  a  true  unit  of  measure  of 
time,  it  is  abscfcitely  indispensable  that  the  motion  of  ro- 
tation of  the  ea|th  upon  its  axis  shall  be  rigorously  uni- 
form and  invariable. 

We  have,  at  present,  in  all  the  active  observatories  in 
the  world,  a  constantly  accumulating  power  of  evidence 
that  the  earth  now  revolves  with  uniform  velocity.  Not 
a  star  passes  the  meridian  wire  of  a  fixed  telescope,  true 
to  the  predicted  moment  of  transit,  without  testifying  to 
the  absolute  uniformity  of  the  earth's  rotation.  So  far, 
then,  as  it  be  possible,  by  human  observation  and  human 
means,  to  determine  any  truth  whatever,  we  are  able  to 
affirm  the  absolute  uniformity  of  the  rotation  of  the 
earth  upon  its  axis.  This  truth  is  affirmed  as  of  to- 
day ;  and  so  far  as  we  can  go  back  in  the  history  of 
accurate  astronomical  observation,  the  same  truth  is 
affirmed  of  the  past;  and  La  Place  informs  us  that,  from 
a  rigorous  investigation  of  the  whole  subject,  he  dis- 
covers that  the  period  of  rotation  of  the  earth  upon  its 
axis  has  not  changed  by  the  hundredth  part  of  one 
second  of  time  in  a  period  of  more  than  two  thousand 


THBEARTH.  73 

years.     We  will  explain  hereafter  the  train  of  reasoning 

*  o 

by  which  this  conclusion  has  been  reached.  We  shall, 
for  the  present,  accept  the  statement  as  a  fact. 

THE   REVOLUTION   OF  THE   EARTH   IN  ITS  ORBIT. — In 

the  examination  already  made  of  the  sun's  apparent  rev- 
olution among  the  fixed  stars,  we  have  found  that  the 
revolution  was  performed  in  the  same  plane,  cutting  out 
of  the  sphere  of  the  fixed  stars  an  exact  'great  circle. 
All  that  was  then  affirmed,  with  reference  to  the  sun's 
apparent  motion,  must  now  be  affirmed  as  belonging  to 
the  earth's  real  motion. 

The  earth,  then,  revolves  around  the  sun  in  the  plane 
of  the  ecliptic,  at  a  mean  distance  of  about  ninety-Jive 
millions  of  miles,  and  in  a,  period  of  about  three  hundred 
and  sixty-Jive  days  and  a  quarter.  It,  of  course,  always 
occupies  a  position  distant  from  the  sun's  place  one  half 
a  circumference,  or  one  hundred  and  eighty  degrees.  The 
changes  of  the  sun's  position  at  noon  in  the  course  of  the 
year,  which  we  have  already  examined,  are  now  readily 
accounted  for  by  the  fact  that  the  earth's  axis  of  rotation 
neither  coincides  with  the  plane  of  the  ecliptic  nor  is 
perpendicular  to  it,  but  is  inclined  under  an  angle,  which 
is  readily  measured,  and  which  is  found  to  undergo  a 
very  slow  change  from  century  to  century.  In  case  the 
earth's  axis  were  perpendicular  to  the  plane  of  the 
ecliptic,  then  the  illuminated  hemisphere  of  the  earth 
would  always  be  bounded  by  a  meridian  circle,  and  every 
inhabitant  of  the  earth  would  find  his  days  and  nights 
precisely  equal,  no  matter  what  his  location  upon  the 
earth's  surface.  If,  on  the  contrary,  the  axis  of  the  earth 
laid  on  the  plane  of  the  orbit,  and  remained  ever  parallel 
to  itself,  then  the  illuminated  hemisphere  would  be 
bounded  by  a  great  circle,  whose  diameter  would  always 


if  4  THE     EARTH. 

be  perpendicular  to  the  earth's  axis,  and  an  equality  of 
day  and  night  would  only  occur  when  the  earth  held  such 
a  position  that  its  axis  would  be  perpendicular  to  the  line 
joining  the  earth's  center  with  the  sun.  Neither  of 
these  cases  exists  in  nature,  and,  as  we  have  already 
seen,  the  annual  sweep  of  the  sun  from  north  to  south, 
and  from  south  to  north,  measures  the  double  inclination 
of  the  earth's  equator  to  the  plane  of  the  ecliptic,  while 
the  length  of  the  day,  as  compared  with  the  nigbt,  com- 
bined with  the  inclination  of  the  solar  beams,  produces 
the  alternation  and  changes  of  the  seasons. 

To  an  inhabitant  of  the  earth's  equator,  the  poles  of 
the  heavens  will  ever  appear  to  lie  in  the  horizon,  and 
while  the  sun  sweeps,  during  the  year,  from  south  to 
north,  and  returns,  yet  the  days  and  nights  are  ever 
equal,  and  a  perpetual  summer  reigns  around  the  equa- 
torial region,  and  a  belt  of  extraordinary  heat  encircles 
the  earth.  Could  an  observer  reach  either  pole  of  the 
earth,  then  the  pole  of  the  heavens  would  occupy  his 
zenith,  all  diurnal  circles  would  be  parallel  to  the  horizon, 
which  would  now  coincide  with  the  equator,  and  so  long 
as  the  sun  was  south  of  the  equator,  (the  observer  being 
at  the  north  pole  of  the  earth),  just  so  long  would  the 
sun  be  below  the  horizon,  and  every  part  of  its  diurnal 
circle  would  be  invisible.  On  the  day  of  the  vernal 
equinox  the  sun  would  just  reach  the  equator  (now  the 
horizon),  and  during  the  entire  revolution  would  be  seen 
sweeping  round  the  horizon,  slowly  rising  above  it.  This 
increase  of  elevation  must  now  progress  up  to  the  summer 
solstice,  and  then  decline  to  the  autumnal  equinox.  The 
daylight  thus  continuing  for  six  entire  months,  and  the 
darkness  for  an  equal  length  of  time.  The«e  theoretic 
statements  are  abundantly  verified  by  the  facts,  as  re- 


THE     EARTH.  75 

ported  by  those  who  have  visited  high  northern  or  south- 
ern latitudes. 

Our  climates  are.  then,  undoubtedly,  determined  by 
the  inclination  of  the  earth's  axis  to  the  ecliptic,  or  what 
amounts  to  the  same  thing,  by  the  inclination  of  the 
earth's  equator  to  the  ecliptic,  the  one  angle  being  the 
complement  of  the  other,  or  what  it  lacks  of  being  ninety 
degrees. 

The  process  employed  by  the  ancients  in  measuring 
the  inclination  of  the  equator  and  ecliptic  we  have  ex- 
plained (chap.  I.),  and  the  same,  with  certain  refine- 
ments, is  still  used  by  the  moderns.  At  the  beginning 
of  the  present  century,  this  angle,  called  the  obliquity 
of  the  ecliptic,  amounted  to  23°  27'  56."  5.  Two  hun- 
dred and  thirty  years  before  Christ,  the  same  angle, 
measured  by  the  Greek  astronomer,  Eratosthenes,  was 
23.°51'.20.//  After  a  lapse  of  370  years,  Ptolemy  found 
the  inclination  to  be  23°.48'.45".  In  the  year  880  of 
our  era,  it  was  23°.35/.00".  In  1690,  Flamsteed  found 
the  same  angle  to  be  23°.29'.00'/,  and  thus  from  century 
to  century  the  change  progresses,  reaching,  however,  a 
limit  beyond  which  it  cannot  pass,  (as  we  shall  presently 
show),  when  it  will  commence  a  reverse  motion,  and  thus 
the  one  plane  slowly  rocks  to  and  fro  upon  the  other  in  a 
calculable,  but  (so  far  as  I  know),  not  yet  calculated 
period. 

The  time  elapsing  from  the  moment  the  earth  is  near- 
est the  sun,  until  it  returns  again  to  the  same  point,  is 
called  an  annomalistic  year.  The  time  from  vernal 
equinox  to  the  same  again,  is  called  a  tropical  year, 
while  the  time  occupied  by  the  earth  in  passing  from  any 
one  point  of  its  orbit,  regarded  as  fixed,  to  the  same  point 
again,  is  called  a  sidereal  year.  These  different  periods. 


76  THE     EARTH. 

at  the  commencement  of  the  current  century,  had  the 
following  values : — 

Mean  Annomalistic  Year,  in  solar  days,  .        .        .    365.2595981 
"     Tropical  "  "  ...     365.2422414 

"     Sidereal  "  "  ...     365,2563612 

These  figures  being  different,  demonstrate  the  great 
and  important  fact  that,  whatever  be  the  precise  figure 
of  the  curve  of  the  earth's  orbit,  the  point  of  nearest  ap- 
proach to  the  sun,  called  the  perihelion,  is  itself  in  mo- 
tion. The  same  is  true  of  the  vernal  equinox,  the  first 
evidently  advancing,  the  second  as  evidently  retrograding, 
and  thus  while  the  advance  of  the  perihelion  increases  the 
length  of  the  annomalistic  year  over  the  sidereal,  the  retro- 
gression of  the  equinox  decreases  the  length  of  the  tropi- 
cal, as  compared  with  the  sidereal  year. 

These  figures  are  presented  as  the  result  of  the  best 
determinations  which  have  been  reached  in  modern  times ; 
but  it  must  not  be  understood  that  the  existence  of  these 
three  different  kinds  of  year  are  the  discovery  of  our  own 
times.  The  discovery  of  the  motion  of  the  vernal  equinox, 
as  we  have  seen,  seems  to  reach  back  to  the  highest  an- 
tiquity, and  was  known  to  all  the  ancient  nations.  The 
rate  of  motion  was  more  exactly  determined  by  the  Greek 
astronomers,  and  hence  the  discovery  has  been  attributed 
to  that  nation.  Modern  observations  have  confirmed  this 
ancient  discovery,  while  modern  physical  science  has 
rendered  a  satisfactory  account  of  this  remarkable  pheno- 
menon, and  has  determined  that  the  equinoctial  point 
completes  the  entire  circuit  of  the  heavens  in  25,868 
years. 

To  ascertain  the  condition  of  the  perihelion  point  as  to 
rest  or  motion,  it  is  only  necessary  to  determine  the  sun's 
place  among  the  fixed  stars  at  the  time  of  any  perihelion, 


THE     EARTH.  77 

and  to  transmit  the  same  to  posterity.  Any  change  of 
the  sun's  place  among  the  stars  at  perihelion,  which  may 
become  known  in  future  ages,  will  demonstrate  the  fact 
that  the  perihelion  is  not  only  in  motion,  but  will  exhibit 
also  the  direction  of  toe  motion,  and  the  rate  of  .advance 
or  recess.  By  a  comparison  of  ancient  observations  with 
modern,  the  perihelion  point  of  the  earth's  orbit  is  found 
to  be  slowly  advancing,  while,  as  we  have  stated  above, 
the  vernal  equinox  is  slowly  retrograding,  at  such  rates 
that  these  two  points  pass  each  other  once  in  20,984 
years.  The  perihelion  coincided  with  the  vernal  equinox, 
as  we  are  able  to  compute  from  their  relative  motions, 
4,089  years  before  the  Christian  era.  Sweeping  onward 
to  meet  the  summer  solstice,  the  perihelion  passed  that 
point  in  the  year  twelve  hundred  and  fifty  of  our  era, 
and  will  meet  the  autumnal  equinox  about  the  year  six 
thousand  four  hundred  and  eighty-three. 

From  the  uniform  rotation  of  the  earth  on  its  axis 
we  obtain,  as  already  stated,  our  unit  of  time.  But  this 
rotation  is  not  sensible  to  man  except  by  its  effect  on  the 
position  of  objects  external  to  the  earth ;  and  hence  we 
determine  the  absolute  period  of  rotation  from  marking, 
the  moment  when  a  fixed  object,  such  as  a  star,  passes 
the  meridian  of  any  given  place.  The  time  elapsing  from 
this  moment  up  to  the  next  passage  of  the  same  object 
across  the  meridian,  supposing  the  earth  to  be  immovable 
as  to  its  central  point,  would  be  the  exact  measure  of 
the  period  of  rotation  of  the  earth  on  its  axis.  Now,  the 
earth's  center,  in  the  space  of  one  day  and  ni^ht,  or  dur- 
ing one  rotation,  actually  passes  over  nearly  2,000,000 
of  miles,  and  it  would  seem  as  though  this  change  of 
position  would  sensibly  affect  the  return  of  our  sUi*  to  the 
meridian,  but  such  is  the  vast  distance  of  the  fare*  stars 


78  THEEAETH. 

ty 

that  visual  rays  sent  to  the  same  star,  from  the  extremi- 
ties of  a  base  line  of  2,000,000  miles  in  length,  are  ab- 
solutely parallel  under  the  most  searching  instrumental 
scrutiny  that  man  has  been  able  to  make.  A  sidereal 
day — the  time  which  elapses  between  the  consecutive  re- 
turns of  the  same  fixed  star  to  any  given  meridian — is  an 
invariable  unit  of  time,  and,  as  such,  is  extensively  used 
in  practical  astronomy;  but  in  civil  life,  inasmuch  as 
all  the  duties  of  life  are  regulated  by  the  return  of  the 
sun  to  the  meridian,  solar,  and  not  sidereal  time,  has  be- 
come the  great  standard  in  the  record  of  all  historic 
and  chronologic  events.  In  case  the  earth  did  not  re- 
volve upon  its  axis,  and  had  no  motion  except  that  of 
revolution  in  its  orbit  around  the  sun,  it  is  manifest  that 
in  the  course  of  one  revolution  the  earth's  axis,  remaining 
parallel  to  itself,  the  circle  dividing  the  illuminated  from 
the  dark  hemisphere  of  earth  would  take  up  successively 
every  possible  position  consistent  with  its  always  remain- 
ing perpendicular  to  the  line  joining  the  centers  of  the 
earth  and  sun.  It  is  manifest,  therefore,  that  by  this 
revolution  around  the  sun  this  luminary  would  be  caused 
to  rise  above  the  horizon  of  any  and  every  place  upon  the 
earth's  surface  successively,  slowly  to  sweep  across  the 
heavens,  and  at  the  end  of  six  months  again  to  sink  be- 
neath the  horizon.  If,  then,  we  define  a  solar  day  to  be 
the  time  which  elapses  from  the  passage  of  the  sun's 
center  across  any  given  meridian  until  it  returns  to  the 
same  meridian  again,  one  such  day  would  evidently  be 
produced  by  the  revolution  of  the  earth  in  its  orbit; 
hence  we  find  a  solar  day  to  be  longer  than  a  sidereal 
day,  because  of  the  fact  that  the  sun's  center  is  brought 
to  the  meridian  later,  in  consequence  of  its  own  ap- 
parent motion.  Indeed,  when  we  come  to  examine  care- 


THBEAKTH.  79 

fully  the  length  of  the  solar  day,  we  find  it  to  he  in  a 
state  of  comparatively  rapid  change,  a  fact  which  we  could 
readily  have  anticipated,  as  we  know  the  apparent  move- 
ment of  the  sun  in  its  orbit,  or  rather  the  real  motion 
of  the  earth,  is  changing  from  day  to  day.  When  the 
earth  is  in  perihelion,  or  nearest  the  sun,  it  then  travels 
with  its  greatest  velocity,  and  passes  over  an  arc  of 
1°  Ol/  9  ".9,  in  a  mean  solar  day,  whereas,  when  the 
earth  is  in  aphelion,  or  furthest  from  the  sun,  it  sweeps 
over  an  arc,  in  the  same  time,  of  only  57'  ll/7.5.  We 
thus  perceive  that  the  length  of  a  true  solar  day  must 
vary  throughout  the  year,  and  for  the  purpose  of  obtain- 
ing a  standard  of  time  the  world  has  adopted  what  is 
called  a  mean  solar  day,  or  a  day  having  the  average 
length  of  all  the  true  solar  days  in  the  year.  All  the 
time-keepers  employed  in  civil  life,  such  as  clocks  and 
chronometers,  are  regulated  to  keep  mean  solar  timej 
while,  for  the  purposes  of  an  observatory,  sidereal  time 
is  in  general  use.  This,  however,  is  slightly  different 
from  the  sidereal  time  already  defined.  The  sidereal 
clock  of  the  observatory,  if  perfectly  true,  would  mark 
Oh.  00m.  OOs.  at  the  moment  the  vernal  equinox  is  on  the 
meridian  of  the  observatory.  It  would  mark  the  same  at 
the  next  return,  and  hence  this  sidereal  day  is  really  a 
vernal  equinox  day.  Now,  as  the  sun's  center  appears 
to  sweep  round  the  whole  heavens  in  the  space  of  one 
year,  and  by  virtue  of  this  motion  passes  across  the  meri- 
dian of  any  place  and  returns  to  the  same  again,  so,  as 
we  have  seen,  the  vernal  equinox  sweeps  around  the 
heavens  in  a  period  of  25,868  years,  and  thus  passes  from 
one  meridian  to  the  same  by  virtue  of  this  motion.  Thus, 
a  vernal  equinox  day  is  shorter  than  a  sidereal  day 
by  an  amount  equal  to  one  day  in  25,868  years,  a 


80  THEMOON. 

quantity  very  minute  indeed,  but  still  insisted  upon,  as 
we  desire  to  impress  upon  the  mind  of  the  reader  the  dif- 
ferences between  these  various  measures  of  time. 

THE  MOON  A   SATELLITE  OP  THE  EAKTH. — In  prose- 

cuting  our  plan  of  investigation  we  must  now  give  some 
account  of  the  moon,  as  she  forms,  astronomically  speak- 
ing, a  part  of  the  planet  which  we  call  the  earth,  and  we 
shall  find  hereafter  that  when  we  speak  of  the  orbit,  in 
which  the  earth  revolves  about  the  sun,  the  real  point 
tracing  that  orbit  is  not  the  center  of  the  earth,  but  a 
point  determined  by  taking  into  consideration  the  fact 
that  the  earth  and  moon  must  be  combined,  as  forming  a 
sort  of  compound  planet,  revolving  about  the  sun.  Of 
all  the  celestial  orbs  furnishing  objects  for  the  investiga- 
tion to  man  no  one  of  them  can  rival  the  moon  in  the 
antiquity  of  its  researches  or  in  the  importance  and  com- 
plexity of  its  revolutions. 

If  it  were  possible  to  trace  the  history  of  astronomical 
discovery,  it  'would  be  found,  beyond  a  doubt,  that  the 
first  positive  fact  ever  revealed  to  the  student  of  the  skies 
was  the  motion  of  the  moon  among  the  fixed  stars.  This 
fact  is  so  obvious  that  any  one  who  chooses  to  mark  the 
moon's  place  by  the  stars  which  surround  her  to-night, 
and  compare  it  with  her  place  on  to-morrow  night,  will 
make  for  himself  the  great  discovery  that  the  moon  is 
sweeping  around  the  heavens  in  a  direction  contrary  to 
that  of  the  diurnal  revolution  of  the  celestial  sphere. 
Thus,  if  we  mark  the  place  of  the  new  moon,  in  th 
evening  twilight,  when  she  appears  as  a  silver  crescent, 
emerging  from  the  sun's  beams,  and  just  visible  above  the 
western  horizon,  we  shall  find  that  on  the  next  evening, 
at  the  same  hour,  her  distance  from  the  horizon  will  have 
been  greatly  increased,  and  this  increase  of  distance  pro- 


T  H  E     M  0  0  N  .  81 

presses  from  night  to  night,  until  we  find  the  moon  actu- 
wlly  rising  in  the  east  at  the  time  the  sun  is  setting  in 
the  west.  On  the  following  night,  at  sunset,  the  moon 
will  not  have  risen,  but  we  will  be  compelled  to  wait 
nearly  an  hour  after  sunset  before  she  becomes  visible 
above  the  eastern  horizon,  and  thus  she  advances  in  her 
orderly  march  among  the  fixed  stars,  until  she  circles 
entirely  around  the  heavens,  passes  through  the  solar 
beams,  and  -reappears  in  the  west  above  the  sun,  as  a  slen- 
der crescent. 

THE  MOON'S  REVOLUTION  IN  HER  ORBIT. — We  have 
already  stated  that,  in  case  it  were  possible  for  the  sun's 
center  to  trace  out  in  its  revolution  among  the  fixed  stars 
a  line  of  golden  light,  visible  to  the  eye  of  man,  this  line 
would  be  a  regular  circle,  perfected  at  the  close  of  one 
revolution,  and  ever  after  repeated,  along  the  same 
identical  track.  Such,  however,  is  not  the  case  with 
our  satellite.  Could  the  moon's  course  be  traced  by 
leaving  behind  her  among  the  stars  a  silver  thread  of 
light,  at  the  completion  of  one  revolution,  this  thread 
would  not  join  on  the  point  of  beginning,  but  would  be 
more  or  less  remote,  and  the  track  described  in  the 
second  and  successive  revolutions  would  not  coincide 
with  that  first  described ;  and  thus  we  should  find  a 
multiplicity  of  silver  lines  sweeping  round  the  circuit  of 
the  heavens,  crossing  each  other,  and  interlacing  in  the 
most  complicated  manner,  and  thus  making  a  girdle,  or 
zone,  of  definite  width,  beyond  whose  limits  the  moon 
could  never  pass.  The  time  occupied  in  completing  one 
of  these  revolutions  from  a  given  star,  until  it  returns  to 
the  great  circle  of  the  heavens,  passing  through  the  axis 
and  this  star  again,  is  soon  found  to  be  variable,  within 
certain  narrow  limits.  This  is  called  a  sidereal  revolu- 

4* 


82  THE     MOON. 

tion,  and  its  mean  value,  at  the  beginning  of  the  present 
century,  is  fixed  at  27d.  7h.  43m.  11.5s.  The  mosS 
obvious  lunar  period,  however,  and  that  doubtless  first 
discovered,  is  that-  called  a  synodicdl  revolution,  and  is 
the  period  elapsing  from  the  occurrence  of  full  moon  to 
full  moon  again,  or  from  new  moon  to  new  moon  again. 
The  average  length  of  this  period,  which  is  also  called  a 
mean  lunation,  amounted,  at  the  epoch  above  mentioned, 
to  29d.  12h.  44m.  2s.  87.  It  is  within  the  limits  of  this 
period  that  the  moon  passes  through  all  those  appearances 
which  we  call 

THE  MOON'S  PHASES.— These  extraordinary  changes  in 
the  physical  aspect  of  the  moon  must  have  perplexed  the 
early  astronomers.  While  the  sun  ever  remained  round 
and  full-orbed  in  all  his  positions  among  the  fixed  stars, 
and  while  all  the  planets  and  bright  stars  shone  with  a 
nearly  invariable  light,  the  moon  passed  from  a  state  of 
actual  invisibility  to  a  condition  in  which  her  disk  was 
as  round  as  that  of  the  sun,  and  thence  gradually  losing 
her  light,  finally  faded  from  the  eye  as  she  approached 
the  solar  orb.  It  was  soon  discovered  that  these  changes 
were  in  some  way  dependent  strictly  upon  the  sun,  and 
not  upon  the  moon's  place  among  the  fixed  stars.  Any 
one  who  chooses  may  verify  this  discovery,  for  by  locat- 
ing the  moon's  place  among  the  fixed  stars  at  the  full, 
and  waiting  her  return  to  the  same  place  again,  it  will 
be  found  that  she  has  not  yet  reached  her  figure  of  a 
complete  circle.  Indeed,  more  than  two  days  are  re- 
quired, after  passing  the  position  occupied  when  last  full, 
before  she  gains  the  point  that  shall  present  us  with  a 
completely  illumined  disk.  The  discovery  of  this  truth 
aided  undoubtedly  in  solving  the  mystery  of  the  moon's 
phases.  It  was  clearly  manifest  that  the  moon  was  re- 


T  H  E     M  0  0  N  .  83 

volving  about  the  earth  in  an  orbit  nearly  circular. 
This  was  evident  from  the  fact  that  the  moon's  apparent 
diameter  did  not  change,  by  any  sensible  amount,  dur- 
ing an  entire  revolution,  which  would  have  been  impos- 
sible in  case  her  approach  to,  or  recess  from  the  earth, 
had  been  very  great  in  any  part  of  her  orbit. 

Another  phenomenon  of  startling  interest  aided  greatly 
in  reaching  a  true  solution  of  the  changes  of  the  moon. 
I  refer,  of  course,  to  solar  and  lunar  eclipses.  We  have 
already  referred  to  solar  eclipses,  as  being  undoubtedly 
produced  by  the  interposition  of  the  dark  body  of  the 
moon  between  the  eye  of  the  spectator  and  the  sun's  disk. 
This  demonstrated  the  fact  that  the  moon  in  her  revolu- 
tion round  the  earth  did  sometimes  cross  the  line  joining 
the  earth's  centre  with  the  sun,  thus  producing  a  central 
solar  eclipse.  It  was  thus  manifestly  possible  for  the 
moon's  center  to  cross  the  same  line  at  a  point  lying  be- 
yond the  earth,  with  reference  to  the  sun.  When  in  this 
position,  a  straight  line  drawn  through  the  center  of  the 
sun,  and  through  the  center  of  the  earth,  and  produced 
onward,  would  pass  through  the  moon's  center,  and  to  a 
person  there  situated,  and  looking  at  the  sun,  he  would 
find  the  solar  surface  covered  by  the  round  disk  of  the 
earth,  thus  producing  to  the  lunarian  a  solar  eclipse. 
When  the  moon  was  thus  situated,  it  was  found  to  be 
shorn  of  a  very  large  proportion  of  its  light,  not  entirely 
fading  from  the  eye,  as  did  the  sun  when  in  total  eclipse, 
but  remaining  indistinctly  visible,  with  a  dull  reddish 
color.  Now,  as  common  observation  teaches  us  that 
every  opaque  object  casts  a  shadow  in  a  direction  oppo- 
site to  the  source  of  light,  it  follows  that  the  earth  must 
cast  a  shadow  in  a  direction  opposite  to  the  sun  ;  and  in 
case  this  shadow  reaehed  as  far  as  the  moon's  orbit,  the 


84  THEMOON. 

moon,  in  taking  up  her  successive  positions,  would  some- 
times pass  into  the  earth's  shadow.  If  self-luminous,  the 
passage  across  the  earth's  shadow  would  occasion  but  a 
trifling  change  in  her  appearance.  If,  however,  her 
light  was  either  wholly  or  in  greater  part  derived  from 
the  sun,  then  in  passing  into  the  earth's  shadow,  the 
stream  of  light  from  the  sun  being  intercepted  by  the 
earth,  the  moon  would  lose  her  brilliancy,  and  could  only 
be  visible  with  an  obscured  lustre.  All  the  phenomena 
presented  in  a  solar  as  well  as  a  lunar  eclipse  combine  to 
demonstrate  that  the  light  of  the  moon  is  not  inherent,  or 
that  this  orb  is  not  a  self-luminous  body ;  and  all  these 
phenomena  were  perfectly  accounted  for  by  admitting 
the  hypothesis  that  the  moon  shines  by  reflecting  the 
light  of  the  sun.  Thus,  during  a  total  solar  eclipse, 
when  the  illuminated  hemisphere  of  the  moon  was  turned 
from  the  earth,  her  hither  side  appeared  absolutely  black, 
while  no  lunar  eclipse  ever  occurred,  except  at  a  time 
when  the  moon's  illuminated  hemisphere  was  wholly  vis- 
ible, or  at  the  full  moon.  In  passing  from  new  moon  to 
full,  it  is  evident,  from  the  slightest  reflection,  that  as 
the  moon  slowly  recedes  from  the  sun,  in  her  movement 
round  the  earth,  she  will  turn  more  and  more  of  her 
illuminated  hemisphere  towards  the  earth,  the  whole  of 
which  will  become  visible  when  she  is  precisely  opposite 
the  sun,  while  the  light  must  decrease  in  a  reverse 
order  in  passing  from  the  full  moon  to  the  new.  Thus, 
all  the  facts  and  phenomena  of  ancient  as  well  as  of 
modern  discovery  combine  to  demonstrate  the  truth  tha 
the  earth's  satellite,  like  the  planets  already  treated  of, 
is  only  visible  by  reflecting  the  light  of  the  sun. 

We  are  ready  by  analogy  to  extend  this  reasoning  to 
embrace  the  earth,  and  to   believe,  that   our  own  earth 


K 

THE     MOON.  85 

shines  to  the  inhabitants  of  other  planets  (if  such  there 
be),  by  reflecting  the  light  of  the  sun.  We  are  not  left, 
however,  to  mere  analogy  to  demonstrate  this  truth,  as 
we  have  the  most  positive  evidence  in  the  phases  of  the 
moon  that  the  earth  does  reflect  the  solar  light.  No 
one  can  have  failed  to  notice  the  fact  that  when  the  moon 
appears  as  a  slender  crescent,  her  entire  disk  may  be 
traced,  faintly  visible  even  to  the  naked  eye ;  but  when 
the  telescope  is  applied,  we  readily  distinguish  in  this 
darkened  part  all  the  outlines  and  prominent  features 
which  become  visible  to  the  unaided  eye  when  the 
moon  is  entirely  full.  This  faint  luminosity  is  beyond  all 
doubt  occasioned  by  the  reflection  back  again  to  the  earth 
of  that  light  which  the  earth  reflects  upon  the  moon;  for 
if  we  consider  the  relative  positions  of  the  sun,  moon,  and 
earth,  we  shall  see  that  at  the  new  moon  the  whole 
illuminated  hemisphere  of  the  earth  is  turned  full  upon 
her  satellite,  and  at  that  time  the  largest  amount  of  light 
from  the  earth  falls  upon  the  surface  of  the  moon.  The 
relative  positions  of  the  bodies  now  slowly  change,  and  as 
the  moon  increases  in  light  by  like  degrees,  the  earth 
loses  in  light ;  and  when  the  moon  becomes  entirely  full, 
the  earth  will  be  to  the  lunarian  entirely  dark,  as  her 
non-luminous  hemisphere  is  then  turned  directly  to  the 
moon. 

We  have  already  stated  that,  during  a  lunar  eclipse, 
the  moon  remains  dimly  visible.  This  is  not  due  to  the 
reflected  light  of  the  sun,  thrown  upon  the  moon  by  the 
earth,  but  arises  from  the  fact  that  the  solar  rays  are  so 
much  bent  out  of  their  course  in  passing  through  the 
earth's  atmosphere,  that  many  of  them  are  still  able  to 
reach  the  moon's  surface,  and  thus  in  some  degree  to  light 
up  her  disk,  even  during  a  central  eclipse. 


86  THE     MOON. 

Amid  all  the  variations  and  changes  which  mark  the 
luminosity  of  the  moon  one  thing  remains  almost  abso- 
lutely invariable.  No  eye  on  earth  has  yet  seen  more 
than  one  half  of  the  lunar  sphere.  The  hemisphere 
now  visible  to  man,  has  (so  far  as  we  know.)  ever  been 
visible,  and,  except  by  the  intrusion  of  some  foreign 
body,  will  ever  remain  turned  toward  the  earth.  There 
are  slight  deviations  from  the  positiveness  of  this  state- 
ment to  which  we  shall  have  occasion  to  allude  hereafter, 
but  the  grand  truth  remains,  that  the  same  hemisphere 
of  the  moon  is  ever  turned  toward  the  earth. 

To  account  for  this  remarkable  fact  we  are  compelled 
to 'acknowledge  a  rotation  of  the  moon  on  her  axis,  in 
the  exact  period  employed  by  her  in  her  revolution  in 
her  orbit.  If  the  moon  had  no  motion  of  rotation  about 
an  axis,  then  in  the  course  of  her  orbital  revolution 
every  portion  of  her  surface  would  come  into  view  suc- 
cessively. 

This  explanation,  which  it  would  seem  ought  to  be  per- 
fectly satisfactory,  has,  in  some  strange  way,  been  not 
only  misunderstood,  but  denied ;  and  yet  should  the  per- 
son most  skeptical  undertake  to  walk  round  a  central  ob- 
ject, always  turning  his  face  to  the  center,  without  as 
well  turning  his  shoulders  and  person,  he  would  receive 
a  positive  'conviction  of  the  truth  of  our  explanation  of 
a  most  practical  character. 

The  physical  cause  of  this  remarkable  fact  in  the 
moon's  history  will  be  duly  considered  hereafter. 

The  same  kind  of  observation  and  reasoning  which  en- 
abled Hipparchus  to  determine  the  eccentricity  of  the 
sun's  apparent  orbit  (the  earth's  real  orbit)  sufficed  to 
enable  this  philosopher  to  determine  the  eccentricity  of 
the  moon's  orbit,  and  the  epicyclical  theory  gave  a 


THE     MOON.  87 

tolerably  fair  account  of  the  most  striking  irregularities 
in  the  moon's  motion.  In  one  respect,  however,  we  find 
a  remarkable  difference  between  the  lunar  and  solar  mo- 
tions. The  position  o"f  the  perihelion  of  the  earth's  orbit 
moves  so  slowly  that  for  a  period  of  even  a  hundred  years 
this  motion  may  be  neglected  without  any  great  error. 
While  the  moon's  apogee,  or  least  distance  from  the  earth, 
was  found  to  be  sweeping  round  the  heavens  with  a  com- 
paratively rapid  motion,  following  the  moon  in  her  course 
among  the  stars,  so  that  while  in  a  period  of  6,585|  days 
the  moon  performed  241  complete  revolutions  with  refer- 
ence to  the  stars,  she  made  but  239  revolutions  with 
regard  to  her  perigee.  Hipparchus  succeeded  in  repre- 
senting this  motion  by  means  of  eccentrics  and  epicycles, 
and  finally  was  able  to  tabulate  the  moon's  places  with 
such  accuracy  as  to  represent  her  positions,  especially  at 
the  new  and  the  full,  so  as  to  predict  roughly  solar  and 
lunar  eclipses. 

Ptolemy  discovered,  500  years  later,  a  new  irregularity 
in  the  moon's  motion,  which  reached  its  maximum  value 
in  what  are  called  the  octants,  that  is,  the  points  half- 
way between  the  new  moon  and  her  first  quarter,  and 
so  on  a  quarter  of  a  circumference  in  advance  round 
the  orbit.  New  attempts  were  made  to  explain  these 
irregularities  by  a  combination  of  circles  and  eccentrics. 
It  was,  finally,  approximately  accomplished,  but  all  these 
facts  thus  accumulating  were  preparing  the  way  for 
the  abandonment  of  an  hypothesis  which  could  only  be 
maintained  by  the  imperfection  of  astronomical  observa- 
tion. 

The  excursions  made  by  the  moon,  north  and  south  of 
the  ecliptic,  or  plane  of  the  earth's  orbit,  were  obviously 
to  be  accounted  for  by  the  fact  that  this  satellite  revolved 


88  THEMOON. 

in  a  plane,  inclined  under  a  certain  angle,  to  the  ecliptic. 
This  angle  was  readily  measured  by  the  ancients,  and, 
though  slightly  variable,  was  fixed  at  the  beginning  of 
our  century  at  5°  &  47".9. 

THE  LUNAR  PAEALLAX  AND  DISTANCE. — The  rude  in- 
struments employed  by  the  early  observers  in  their  as- 
tronomical observations  were  insufficient  for  any  delicate 
work,  and  hence  we  find  them  quite  ignorant  of.  the 
absolute  value  of  even  the  moon's  parallax,  a  quantity 
which  far  exceeds  any  other  parallactic  angle  of  the 
solar  system.  We  have  already  shown  (Chap.  I.)  how 
the  distance  of  an  inaccessible  object  may  be  obtained  by 
measuring  the  angles  formed  at  the  extremities  of  a  given 
base  line,  by  visual  rays  drawn  to  the  object.  In  case 
the  base  line  be  very  short  in  proportion  to  the  distance 
to  be  measured,  the  sum  of  the  two  angles  thus  measured 
will  approach  in  value  180°,  and  the  angle  at  the  distant 
object  formed  by  the  visual  rays  becomes  smaller  in  pro- 
portion to  its  distance.  In  our  attempts  to  measure  the 
solar  parallax,  using  the  earth's  diameter  as  a  base,  it 
was  found  that  the  delicacy  of  modern  instruments  was 
not  adequate  to  so  difficult  a  task.  This,  however,  is  not 
the  case  when  we  come  to  apply  them  in  the  determina- 
tion of  the  lunar  parallax.  Indeed,  the  moon  is  found  to 
be  so  near  the  earth  that  visual  rays,  drawn  from  specta- 
tors at  different  parts  of  the  earth,  not  very  remote  from 
each  other,  to  the  moon's  center,  form  with  each  other 
sensible  angles ;  and  thus  the  moon,  viewed  from  differ- 
ent stations,  is  projected  among  different  stars.  When 
the  moon's  center  is  in  the  absolute  horizon,  (that  is,  in 
a  plane  passing  through  the  center  of  the  earth  and 
perpendicular  to  the  earth's  radius  drawn  to  the  place 
of  the  spectator),  lines  drawn  from  the  center  of  the 


NORTH  WESTERN  BOUNDARY  OF  MARE  SERENITATIS 
1860FEBR    27  8  H. P.M. ALBANY  TIME 
DUDLEY  OBSERVATORY. 


T  H  E  M  o  o  y .  89 

earth  and  from  the  eye  of  the  observer  unite  at  the 
moon's  center,  under  an  angle  called  the  moon's  horizon- 
tal  parallax.  In  case  the  moon's  distance  from  the 
earth  were  constant,  this  angle  would  also  be  invariable. 
This,  however,  is  not  the  case,  and  we  find  the  horizon- 
tal parallax  reaches  a  maximum  value  equal  to  1°  1'  24", 
when  the  moon  is  nearest  the  earth,  and  a  minimum 
value  of  0053'48,"  when  most  remote — the  average 
value  being  0°  57'  00".9.  These  angles  give  for  the 
moon's  mean  distance  from  the  earth  237,000  miles. 

As  all  the  computed  places  of  the  planetary  orbs  as- 
sume the  spectator  to  occupy  the  earth's  center,  we  read- 
ily perceive  that,  in  the  case  of  the  moon,  the  computed 
and  observed  places  would  never  agree,  except  in  one  in- 
stance, namely,  that  in  which  a  line  joining  the  center  of 
the  earth  with  the  moon's  center  passes  through  the  place 
of  the  observer,  or  when  the  moon's  center  is  exactly  in 
the  zenith.  The  effect  of  parallax  on  the  apparent  place 
of  the  moon  is  to  sink  it  below  the  position  it  would  have 
held  in  case  it  were  seen  from  the  earth's  center. 

Knowing  the  actual  distance  of  the  moon,  her  real 
diameter  is  readily  determined,  and  is  found  to  be 
about  2,160  miles  ;  hence  her  volume  is  about  one- 
forty-ninth  part  of  that  of  the  earth.  We  shall  have 
occasion  hereafter  to  resume  our  examination  of  the 
moon's  motions  when  we  come  to  discuss  the  physical 
causes  by  whose  power  the  planetary  orbs  are  held  in 
dynamical  equilibrium,  and  are  retained  in  their  orbits. 
We  now  proceed  to  examine  the  physical  constitution  of 

THE     MOOX,    AS    REVEALED    BY    THE     TELESCOPE. — 

The  splendid  instruments  which  modern  skill  and  science 
have  furnished  for  the  examination  of  the  distant  worlds 
so  far  increase  the  power  and  reach  '.f  human  vision, 


90  THEMOON. 

in  the  case  of  the  moon,  as  to  bring  this  satellite  of  the 
earth  comparatively  within  our  reach.  A  telescope 
which  bears  a  magnifying  power  of  one  thousand  times, 
applied  to  the  examination  of  the  moon's  surface,  ena- 
bles the  observer  to  approach  to  within  237  miles  of 
this  extraordinary  world,  and  even  this  distance,  under 
the  most  favorable  circumstances,  may  be  reduced  by 
one-half.  This,  perhaps,  is  the  nearest  approach  ever 
made  to  the  moon,  and  it  is  at  a  distance  of  say  150 
miles  that  we  are  permitted  to  stand  and  examine  at 
our  leisure  the  features  which  diversify  the  surface  of 
our  satellite.  No  subject  has  excited  so  deep  an  in- 
terest from  mere  curiosity,  as  that  involved  in  the  actual 
condition  of  the  moon's  surface.  Every  one  desires  to 
know  if  the  other  worlds  are  like  our  own.  Have  they 
oceans  and  seas,  lakes,  rivers,  islands,  and  continents? 
Does  their  soil  resemble  our  own  ?  Does  vegetable  life 
there  manifest  itself  in  every  variety  of  grass  and  flowers, 
and  shrub  and  tree?  Are  there  extended  forests  and 
spicy  groves,  filled  with  multitudinous  animals,  in  these 
far  oif  worlds  ?  And,  above  all,  are  these  bright  orbs 
inhabited  by  rational  intelligent  beings  like  man  ?  The 
earnest  desire  to  obtain  responses  to  these  and  like  ques- 
tions, caused  to  be  received,  many  years  since,  with  the 
most  wonderful  delight  and  credulity,  a  statement  put 
forth  in  America,  giving  professedly  the  details  of  lunar 
discoveries,  said  to  have  been  made  by  Sir  John  Herschel 
at  the  Cape  of  Good  Hope,  in  which  all  tbese  questions 
were  most  satisfactorily  answered.  We  need  hardly  say 
how  great  was  the  disappointment  when  these  pretended 
discoveries  proved  to  be  but  fanciful  inventions.  When 
we  call  to  rnind  that  with  a  telescope  magnifying  2,000 
times  we  are  still  separated  from  the  moon  120  miles,  we 


THEMOON.  91 

readily  perceive  the  utter  impossibility  of  solving  at  pres- 
ent, directly  by  vision,  the  problem  of  the  moon's  habita- 
bility.  We  know  not  what  may  be  accomplished  by  human 
genius  and  human  invention,  and  after  the  production  of 
so  marvellous  an  instrument  as  a  telescope  capable  of 
transporting  the  beholder  to  within  120  miles  of  the  sur- 
face of  a  body  actually  removed  237,000  miles,  we  will 
not  presume  to  set  any  specific  limits  to  future  effort. 
We  can  only  say  that  the  telescope  must  become  vastly 
improved  in  its  powers  of  definition  and  development  be- 
fore we  can  hope  to  satisfy  ourselves,  from  actual  inspec- 
tion, that  our  satellite  is  or  is  not  inhabited  by  a  race 
with  any  of  the  faculties  which  distinguish  man. 

Let  us  see  what  has  actually  been  accomplished  by 
telescopic  investigation,  and  although  it  falls  far  short 
of  satisfying  the  curiosity  of  our  nature  we  shall  find 
much  to  interest  and  astonish.  We  can  affirm,  then, 
that  the  surface  of  our  satellite  is  diversified  with  hill 
and  dale,  with  lofty  mountains  and  mighty  cavities,  with 
extensive  plains  and  isolated  mountain,  peaks,  not  very 
unlike  the  same  features  presented  by  our  earth.  The 
hemisphere  of  the  moon,  visible  to  man,  has  been  studied 
and  mapped  with  the  greatest  care.  Indeed,  its  eleva- 
tions and  depressions  have  been  accurately  modeled,  the 
mountain  elevations  have  been  measured,  and  the  depths 
of  the  mighty  cavities  which  distinguish  her  surface  have 
all  been  carefully  determined.  These  measures  all  de- 
pend on  the  fact  that  the  moon  receives  its  light  from 
the  sun,  and  presents  its  surface  to  that  or!)  under  every 
angle  in  the  course  of  its  revolution.  The  mountains  of 
the  moon,  like  those  of  the  earth,  have  their  summits 
first  lighted  by  the  rays  of  the  rising  sun,  while  all  the 
plain  beneath,  and  their  rough  and  rugged  sides,  are  in 


92  THE     MOON. 

the  deepest  darkness.  These  summits,  when  so  illumin- 
ated, glow  and  sparkle  with  a  dazzling  beauty  unsur- 
passed. As  the  sun  rises,  we  perceive  distinctly  the 
black  shadow  of  the  mountain  falling  to  a  great  distance 
on  the  plain  below.  These  shadows  slowly  decrease 
in  length,  and  their  outlines  gradually  creep  up  the 
mountain  side  as  the  sun  reaches  the  moon's  meridian. 
When  the  sun  begins  to  decline  the  shadows  fall  in  the 
•opposite  direction,  slowly  extend  their  black  masses  over 
the  distant  plains,  and  darkness  finally  gathers  round  the 
mountain  sides,  till  again  the  summit  is  alone  illumined 
by  the  rays  of  a  setting  sun.  It  is  by  means  of  those 
shadows,  whose  lengths  are  readily  determined  by  nlicro- 
metrical  measures,  that  we  are  enabled  to  determine  the 
heights  of  the  lunar  mountains  and  the  depths  of  the 
lunar  cavities.  This  process  is  not  more  difficult  than  to 
determine  the  elevation  of  a  church  steeple  or  other  lofty 
object  by  the  length  of  its  shadow  cast  upon  a  horizontal 
plane  below.  The  altitude  of  the  sun  above  the  horizon 
at  noon  will  give  the  direction  of  the  visual  ray  passing 
from  the  summit  of  the  object  to  the  extremity  of  its 
shadow.  Knowing  the  value  of  this  angle,  and. the  meas- 
ured length  of  the  shadow  cast,  we  have  at  once  the 
means  of  determining  the  elevation  of  the  object  under 
examination.  These  simple  principles  are  readily  trans- 
ferred to  the  determination  of  the  heights  and  depths  of 
the  lunar  surface,  while  the  figure  of  the  shadow  cast  by 
the  summits  of  a  mountain  range  on  an  extended  plain 
below,  gives  to  us  almost  as  perfect  a  knowledge  of  the 
actual  forms  of  the  lunar  mountains  as  though  it  were 
possible  actually  to  tread  their  lofty  summits. 

We  find  upon  the  moon's  surface  a  range  of  mountains 
lifting  themselves  above  a  level  country  and  extending 


LUNAR      SURFACE 


CASSENDIUS,DUDLEY  OBSERVATORY 
JAN, i860. 


THEMOON.  93 

nearly  two  hundred  miles,  which  have  received  the  name 
of  the  Appenines.  This  mountain  range  comes-into  the 
sunlight  just  after  the  moon  has  passed  its  first  quarter, 
and  is  then  one  of  the  fines';  objects  that  the  telescope  re- 
veals to  the  eye  of  man.  The  brilliancy  of  the  illumin- 
ated heights  and  ridges,  the  absolute  blackness  of  the  deep, 
rocky  chasms,  the  lofty  peaks,  the  rugged  precipices,  and 
the  deep  shadows,  all  combine  to  increase  the  natural 
grandeur  of  this  extensive  mountain  range.  Let  it  not 
be  imagined  that  details  in  such  a  scene,  such  as  actual 
individual  rocks,  of  definite  form  and  outline,  are  to  be 
seen;  but  as  lights  and  shades  produce  the  forms  of 
every  surface,  so  these  lights  and  shadows  on  the  moon 
bring  out  the  absolute  forms  in  the  most  distinct  and  per- 
fect manner.  The  contrasts  between  the  dark  and  illum- 
inated parts  of  the  moon  are  far  deeper  and  stronger  than 
on  the  earth.  This  arises  from  the  fact  that  the  sunlight 

j  on  the  moon  is  not  reflected  or  refracted  by  an  atmosphere 
such  as  surrounds  the  earth.  The  twilight  which  attends 
the  setting  sun  and  the  dawn,  which  so  beautifully  an- 

,  nounces  the  coming  of  day,  does  not  exist  for  the  lunari- 
ans. If  any  eye  beholds  the  rising  of  the  mighty  orb  of 
day  from  those  lofty  lunar  summits  which  are  first  illu- 
mined by  his  horizontal  beams,  no  gentle  flashings,  or 
rosy  tints,  or  purple  hues,  but  from  intense  darkness 
there  is  an  instantaneous  burst  of  brilliant  sunlight.  The 
beauty  of  our  dawns  and  twilights  is  due  to  the  atmos- 

'  phere  which  surrounds  the  earth,  and  while  we  cannot 
affirm  that  no  such  atmosphere  surrounds-  our  satellite, 
we  are  certain  that  whatever  gaseous  envelope  may  sur- 
round the  moon  on  its  hither  side,  its  density  cannot  com- 
pare with  that  of  the  terrestrial  atmosphere.  Under  very 

.  favorable  circumstances,  with  the  great  refractor  of  tho 


94  THEMOON, 

Cincinnati  Observatory,  the  author  has  either  seen,  or 
fancied  he  saw,  a  faint  penumbra  edging  the  dark  moun- 
tain shadows,  and  clinging  to  the  black  outline,  as  it 
slowly  crept  up  the  mountain  side,  as  the  sun  rose  higher 
and  higher.  We  shall  return  to  this  subject  when  we 
come  to  treat  of  certain  peculiarities  attending  the  eclipse 
of  the  sun,  and  the  occultation  of  stars  by  the  moon. 

Some  of  the  mountains  of  the  moon  reach  an  elevation 
of  8  to  10,000  feet  above  the  general  level.  Here  and 
there  we  find  insulated  peaks  rising  abruptly  from  ex- 
tended plains  to  a  height  of  6  or  7,000  feet,  and  in  the 
early  lunar  morning  flinging  their  long,  sharp,  black 
shadows  to  a  vast  distance. 

But  the  most  remarkable  feature  presented  in  the  lu- 
nar surface  is  the  tremendous  depths  of  some  of  the  cavi- 
ties, and  their  immense  magnitude.  Some  of  them  ex- 
tend beneath  the  general  level  of  the  country  to  a  depth 
of  10  to  17,000  feet,  and  their  rough,  misshapen,  precipi- 
tous sides,  exhibit  scenes  of  rugged  sublimity  to  which 
earth  presents  no  parallel.  Of  these  cup-shaped  cavities, 
especially  in  the  southern  portion  of  the  lunar  hemisphere, 
the  number  is  beyond  credibility ;  and,  in  case  we  ad- 
mit them  to  be  the  extinct  craters  of  once  active  volca- 
noes, we  are  forced  to  the  conclusion  that  convulsions, 
such  as  the  earth  is  a  stranger  to,  have  shaken  the  outer 
crust  of  our  satellite  into  a  hideousness  of  form  unknown 
in  any  region  of  our  planet.  Some  of  these  deep  cavities 
are  nearly  circular  in  figure,  and  with  diameters  of  all 
magnitudes  up  to  twenty  miles.  Very  often  the  in- 
terior will  exhibit  a  uniformly  shaded  surface,  and  in 
the  center  a  conical  mountain  will  lift  itself  far  above  this 
level  plain.  That  these  convulsions  are  of  different  ages 
is  clearly  manifest  from  the  fact  that  their  outlines  very 


THEMOOS.  95 

often  overlap  one  another,  and  the  oldest  and  the  newest 
formations  are  thus  distinctly  traced  by  the  eye  of  man. 
So  sharp  and  positive  is  the  outline  of  these  extraordinary 
objects  that  one  cannot  but  feel  that  some  sudden  burst- 
ing forth  might  even  occur  while  under  telescopic  exam- 
ination. Once  indeed,  while  closely  inspecting  these 
seemingly  volcanic  mountains  and  craters  of  the  moon,  I 
was  startled  by  a  spectacle  which,  for  a  moment,  produced 
upon  the  mind  a  most  strange  sensation.  A  mighty 
bird,  huge  in  outline  and  vast  in  its  proportions,  suddenly 
lifted  itself  above  the  moon's  horizon  and  slowly  ascended 
in  its  flight  towards  the  moon's  center.  It  was  no  lunar 
bird,  however,  but  one  of  earth,  high  up  in  the  heavens, 
winging  its  solitary  flight  in  the  dead  of  night,  and  by 
chance  crossing  the  field  of  vision  and  the  lunar  disk. 

Before  the  power  of  the  telescope  had  reached  its  pres- 
ent condition  of  perfection  the  darker  spots  of  the  moon 
were  assumed  to  be  seas  and  oceans ;  but  the  power  now 
applied  to  the  moon  demonstrates  that  there  cannot  exist 
at  this  time  any  considerable  body  of  water  on  the  hemi- 
sphere visible  from  the  earth.  And  yet  we  find  objects 
Buch,  that  in  case  we  were  gazing  upon  the  earth  from 
the  moon,  possessing  our  actual  knowledge  of  the  earth's 
lakes  and  rivers,  we  should  pronounce  them,  without 
hesitation,  lakes  and  rivers.  There  is  one  such  object 
which  I  will  describe  as  often  seen  through  the  Cincinnati 
Refractor.  The  outline  is  nearly  circular,  with  a  lofty 
range  of  hills  on  the  western  and  south-western  sides. 
This  range  gradually  sinks  in  the  east,  and  a  beautiful 
sloping  beach  seems  to  extend  down  to  the  level  surface 
of  the  inclosed  lake  (as  we  shall  call  it,  for  want  of  other 
language).  With  the  highest  telescopic  power,  under 
the  most  favorable  circumstances,  I  never  could  detect 


96  THE     MOON. 

the  slightest  irregularity  in  the  shading  of  the  surface  of 
the  lake.  Had  the  cavity  been  filled  with  quick-silver 
and  suddenly  congealed  or  covered  with  solid  ice,  with  a, 
covering  of  pure  snow,  the  shading  could  not  be  more 
regular  than  it  is.  To  add,  however,  to  the  terrene  like- 
ness, into  this  seeming  lake  there  flows  what 'looks  exactly 
as  a  river  should  at  such  a  distance.  That  there  is  an 
indentation  in  the  surface,  exactly  like  the  bed  of  a  river, 
extending  into  the  country,  (with  numerous  islands,)  for 
more  than  a  hundred  miles,  and  then  forking  and  sepa- 
rating into  two  distinct  branches,  each  of  which  pursues 
a  serpentine  course  for  from  thirty  to  fifty  miles  beyond 
the  fork,  all  this  is  distinctly  visible.  I  may  say,  indeed, 
that  just  before  entering  the  lunar  lake  this  lunar  river 
is  found  to  disappear  from  sight,  and  seems  to  pass  be- 
neath the  range  of  hills  which  border  the  lake.  The  re- 
gion of  country  which  lies  between  the  forks  or  branches 
of  this  seeming  river,  is  evidently  higher,  and  to  the  eye 
appears  just  as  it  should  do,  so  as  to  shed  its  water  into 
the  stream  which  appears  to  flow  in  the  valley  below. 
The  question  may  be  asked,  why  is  this  not  a  lake  and  a 
river?  There  is  no  lunar  atmosphere  on  the  visible 
hemisphere  of  the  moon,  such  as  surrounds  the  earth,  and 
if  there  were  water  like  ours  on  the  moon,  it  would  be 
soon  evaporated,  and  would  produce  a  kind  of  vaporous 
atmosphere,  which  ought  to  be  shown  in  some  of  the 
many  phenomena  involving  the  moon,  but  has  not  yet 
been  detected.  What,  then,  shall  we  call  the  objects  de- 
scribed? I  can  only  answer  that  this  phenomenon,  with 
many  other,  presented  by  the  lunar  surface,  has  thus  far 
baffled  the  most  diligent  and  persevering  efforts  to  ex- 
plain. In  some  of  these  cavities,  where  the  tinting  of 
the  level  surface  is  so  perfect  with  an  ordinary  telescope, 


THE    MOON.  97* 

when  examined  with  instruments  of  the  highest  power, 
we  detect  small  depressions  in  this  very  surface,  cup- 
shaped,  and  in  all  respects  resembling  the  form  and  fea- 
tures of  the  principal  cavity.  These  hollow  places  are 
clearl  v  marked  by  the  shadows  cast  on  the  interior  of  the 
edges,  which  change  as  the  sun  changes,  and  seem  to 
demonstrate  that  these  level  surfaces  do  not  belong  to  a 
fluid  but  to  a  solid  substance. 

Among  what  are  called  the  volcanic  mountains  of  the 
moon  are  found  objects  of  special  interest.  One  of  them, 
named  Copernicus,  and  situated  not  far  from  the  moon's 
equator,  is  so  distinctly  shown  by  the  telescope,  that  the 
external  surface  of  the  surrounding  mountains  presents  the 
very  appearance  we  would  expect  to  find,  in  mountains 
formed  by  the  ejecting  from  the  crater,  of  immense  quan- 
tities of  lava  and  melted  matter,  solidifying  as  it  poured 
down  the  mountain  side,  and  marking  the  entire  external 
surface  with  short  ridges  and  deep  gullies,  all  radiating 
from  a  common  center.  Can  these  be,  indeed,  the  over- 
flowing of  once  active  volcanoes?  Sir  William  Her- 
schel  once  entertained  the  opinion  that  they  were,  and, 
with  his  great  reflecting  telescope,  at  one  time  discovered 
what  he  believed  to  be  the  flames  of  an  active  volcano 
on  the  dark  part  of  the  new  moon.  More  powerful  in- 
struments have  not  confirmed  this  discovery,  and  although 
a  like  appearance  of  a  sort  of  luminous  or  brilliant  spot, 
has  been  seen  by  more  than  one  person,  it  is  almost  im- 
possible to  assert  the  luminosity  to  be  due  to  a  volcano  in 
a  state  of  irruption,  but  is  more  commonly  supposed  to  be 
some  highly  reflective  surface  of  short  extent,  and  for  a 
time  favorably  situated  to  throw  back  to  us  the  earth- 
shine  of  our  own  planet. 

From  some  of  these  seeming  volcanoes  there  are  streaky 

5 


98  THE     MOON. 

radiations  or  bright  lines,  running  from  a  common  center, 
and  extending  sometimes  to  great  distances.  These  have 
by  some  been  considered  to  be  hardened  lava  streams  of 
great  reflective  power,  but,  unfortunately  for  this  hypo- 
thesis, they  hold  their  way  unbroken  across  deep  valleys 
and  abrupt  depressions,  which  no  molten  matter  flowing 
as  lava  does,  could  possibly  do.  To  me  they  more  re- 
semble immense  upheavals,  forming  elevated  ridges  of  a 
reflecting  power  greater  than  that  of  the  surrounding 
country. 

We  find  on  the  level  surfaces  a  few  very  direct  citts,  as 
they  may  be  called,  not  unlike  those  made  on  our  planet 
for  railway  tracks,  only  on  a  gigantic  scale,  being  more 
than  a  thousand  yards  in  width,  and  extending  in  some 
instances  over  a  hundred  miles  in  length.  What  these 
may  be  it  is  useless  to  conjecture.  We  cannot  regard 
them  as  the  work  of  sentient  beings,  and  must  rather 
consider  them  as  abrupt  depressions  or  faults  in  the  lunar 
geography. 

THE  MOON'S  CENTER  OF  FIGURE. — The  wonderful 
phenomena  presented  to  the  eye  on  the  visible  hemisphere 
of  the  moon  have  been  rendered  in  some  degree  expli- 
cable by  a  remarkable  discovery  recently  made,  that  the 
center  of  gravity  of  the  moon  does  not  coincide  with  the 
center  of  figure.  This  is  not  the  place  to  explain  how 
this  fact  has  been  ascertained.  It  is  now  introduced  to 
Dresent  its  effect,  on  the  hither  portion  of  the  lunar  orb. 

If  the  material  composing  the  moon  was  lighter  in  one 
hemisphere  than  the  other,  it  is  manifest  that  the  center 
of  gravity  would  fall  in  the  heavier  half  of  the  globe. 
For  instance,  a  globe  composed  partly  of  lead  and  partly 
of  wood  could  not  have  the  center  of  gravity  coincident 
with  the  center  of  the  globe ;  but  it  would  lie  somewhere 


T  H  E     M  0  0  N  99 

in  the  leaden  hemisphere.  So  it  now  appears  that  the 
center  of  gravity  of  the  moon  is  more  than  33  miles  from 
the  center  of  figure,  and  that  this  center  of  gravity  falls 
in  the  remote  hemisphere,  which  can  never  be  seen  by 
mortal  eye. 

Now,  the  center  of  gravity,  is  the  center  to  which  all 
heavy  bodies  gravitate.  About  it  as  a  center  the  lunar 
ocean  and  the  lunar  atmosphere,  in  case  such  exist, 
would  arrange  themselves,  and  the  lighter  hemisphere 
would  rise  above  the  general  level,  as  referred  to  the 
center  of  gravity,  to  an  extreme  height  of  33  miles. 
Admitting  this  to  be  true,  and  as  we  shall  see  hereafter 
the  fact  appears  to  be  well  established,  we  can  readily 
perceive  that  no  water,  river,  lake  or  sea,  should  exist 
on  the  hither  side  of  the  moon,  and  no  perceptible  atmos- 
phere can  exist  at  so  great  an  elevation.  Even  vegetable 
life  itself  could  not  be  maintained  on  a  mountain  tower- 
ing up  to  the  enormous  height  of  33  miles ;  and  hence 
we  ought  to  expect  the  hither  side  of  our  satellite  to  pres- 
ent exactly  such  an  appearance  as  is  revealed  by  tele- 
scopic inspection. 

If  the  centers  of  gravity  and  figure  ever  coincided  in 
the  moon,  and  the  change  of  form  has  been  produced  by 
some  great  convulsion,  which  has  principally  expended 
its  force  in  an  upheaval  of  the  hither  side  of  the  globe, 
then  we  can  account  for  the  rough,  broken,  and  shat- 
tered condition  of  the  visible  surface.  Lakes  and  rivers 
may  once  have  existed,  active  volcanoes  might  once  have 
poured  forth  their  lava  streams,  while  now  the  dry  and 
desolate  beds  and  the  extinct  craters  are  only  to  be 
seen. 

The  consequences  which  flow  from  this  singular  dis- 
covery as  to  the  figure  of  our  satellite  are  certainly  very 


100  THE     MOON 

remarkable,  and  will  doubtless  be  traced  with  deep  interest 
in  future  examinations. 

OCCULT ATIONS. — As  the  moon  is  very  near  the  earth, 
and  her  disk  covers  a  very  considerable  surface  in  the  heav- 
ens in  her  sweep  among  the  fixed  stars,  she  must  of  course 
cross  over  a  multitude  of  stars  in  her  revolutions.  A  star 
thus  hidden  by  the  moon  is  said  to  be  occulted,  and  these 
occultations  are  phenomena  of  special  interest  on  many 
accounts.  As  a  general  thing,  a  star  even  of  the  first 
magnitude,  in  passing  under  the  dark  limb  of  the  moon, 
vanishes  from  the  sight  instantaneously,  as  though  it 
were  suddenly  stricken  from  existence,  and  at  its  re- 
appearance its  full  brilliancy  bursts  at  once  on  the  eye. 
This  demonstrates  the  fact  that  the  stars  can  be  nothing 
more  than  luminous  points  to  our  senses,  even  when 
grasped  by  the  greatest  telescopic  power. 

A  strange  appearance  sometimes  attends  the  occulta- 
tion  of  stars  by  the  moon.  The  star  comes  up  to  the 
moon's  limb,  entirely  vanishes  for  a  moment,  then  re- 
appears, glides  on  the  bright  limb  of  the  moon  for  a 
second  or  more,  and  then  suddenly  fades  from  the  sight. 

This  phenomenon,  as  also  another  of  most  startling 
character  attending  sometimes  the  total  eclipse  of  the  sun, 
when  blood-red  streaks  in  radiations  are  found  to  shoot 
suddenly  from  behind  the  moon's  limb,  are  supposed  by 
some  to  demonstrate  the  existence  of  a  lunar  atmosphere. 
Much  attention  has  been  bestowed  on  the  total  eclipses 
of  the  sun  during  the  past  twenty  years,  for  the  express 
purpose  of  solving,  if  possible,  these  mysterious  radia- 
tions of  red  light.  Some  entertain  the  opinion  that  they 
are  due  to  the  colored  glasses  used  to  soften  the  intense 
solar  light,  as  seen  through  the  telescope.  We  can  only 
say  that^these  phenomena  remain  without  satisfactory 


THE     MOON.  101 

explanation,  and  that  the  physical  condition  of  the  moon 
is  yet  a  problem  of  the  deepest  interest.  We  can  assert 
the  irregularities  of  her  surface,  her  deep  cavities  and 
lofty  elevations,  her  extended  plains  and  abrupt  moun- 
tain peaks,  but  beyond  this  our  positive  knowledge  does 
not  extend. 

We  shall  resume  the  consideration  of  our  satellite 
when  we  come  to  discuss  the  great  theory  of  universal 
gravitation. 


CHAPTER  V. 

MABS,    THE    FOURTH    PLANET    IN    THE    ORDER    OF  DIS- 
TANCE FROM  THE  SUN. 


PHENOMENA  or  MARS  DIFFICULT  TO  EXPLAIN  WITH  THE  EARTH  AS  THE  CENTEB 
OF  MOTION. — COPERNICAN  SYSTEM  APPLIED. — EPICYCLE  OF  MARS.— OBETTEB 
INSTRUMENTS  AND  MORE  ACCURATE  OBSERVATIONS. — TYOHO  AND  KEPLEE. — 
KEPLER'S  METHOD  OF  INVESTIGATION. — CIRCLES  AND  EPICYCLES  EXHAUSTED. 
— THE  ELLIPSE. — ITS  PROPERTIES. — THE  ORBIT  OF  MAKS  AN  ELLIPSE.— 
KEPLER'S  LAWS. — ELLIPTICAL  OKISITS  OF  THE  PLANETS. — THE  ELEMENTS  OF 
THE  PLANETARY  ORBITS  EXPLAINED. — How  THESE  ELEMENTS  ARE  OBTAINED. 
— KEPLER'S  THIRD  LAW. — VALUE  OF  THIS  LAW. — THE  PHYSICAL  ASPECT  OF 
MARS. — Sxow  ZONES. — ROTATION  OF  THE  PLANET. — DIAMETER  AND  VO- 
LUME.— SPECULATION  AS  TO  ITS  CLIMATE  AND  COLOR. 


THIS  planet  is  distinguished  to  the  naked  eye  by  its 
brilliant  red  light,  and  is  one  of  the  planets  discovered 
by  the  ancients.  To  the  old  astronomers  Mars  presented 
an  object  of  special  difficulty.  Revolving  as  it  does  in 
an  orbit  of  great  eccentricity,  sometimes  receding  from 
the  earth  to  a  vast  distance,  then  approaching  so  near  as 
to  rival  in  brilliancy  the  large  planets,  Jupiter  and  Venus, 
on  the  old  hypothesis  of  the  central  position  of  the  earth, 
and  the  uniform  circular  motion  of  the  planets,  Mars 
presented  anomalies  in  his  revolution  most  difficult  of 
explanation. 

These  complications  were  measurably  removed  by  the 
great  discovery  of  Copernicus,  which  released  the  earth 
from  its  false  position,  and  gave  to  Mars  its  true  center, 
the  sun ;  but  even  with  this  extraordinary  advance  in  the 
direction  towards  a  full  solution  of  the  mysterious  move- 


MARS. 


103 


ments  of  this  planet,  there  remained  many  anomalies  of 
motion  of  a  most  curious  and  incomprehensible  character. 
It  will  be  remembered  that  Copernicus,  in  adopting  the 
sun  as  the  center  of  the  planetary  orbits,  was  compelled 
to  retain  the  epicycle  of  the  old  Greek  theorists,  to  ac- 
count for  the  facts  which  still  distinguished  the  planetary 
revolutions.  As  in  the  revolution  of  the  earth  about  the 


sun  there  was  an  approach  to  and  recess  from  this  central 
orb,  so  in  the  revolution  of  Mars  it  was  manifest  that 
there  was  a  vast  difference  between  the  aphelion  and  peri- 
helion distances  of  the  planet.  The  epicycle  was  then 
retained  to  account  for  this  anomaly  in  the  motion  of 
Mars ;  and  it  will  be  readily  seen  from  the  figure  above 
how  this  hypothesis  rendered  a  general  explanation  of  the 
facts  presented  for  examination. 


104  MARS. 

The  large  circle,  having  the  sun  for  its  center,  repre- 
sents the  orbit  of  Mars,  that  is,  a  circle  whose  radius  is 
equal  to  the  average  or  mean  distance  of  the  planet. 
The  small  circles  represent  the  epicycle,  in  the  circum- 
ference of  which  the  planet  revolves  with  an  equable  mo- 
tion, while  its  center  moves  uniformly  round  on  the  cir- 
cumference of  the  large  circle.  When  the  planet  is  at  A, 
it  is  in  perihelion,  or  nearest  the  sun.  While  the  center 
of  the  epicycle  performs  a  quarter  revolution,  the  planet 
also  performs  in  its  epicycle  a  quarter  of  a  revolution, 
and  reaches  the  position  B.  A  half  revolution  brings  it 
to  aphelion  in  C,  and  three  quarters  of  a  revolution  in 
the  epicycle  locates  the  planet  at  D,  and  an  entire  revo- 
lution brings  it  again  to  A,  the  point  of  departure.  Thus 
it  will  be  seen  that  the  planet  must  describe  an  oval  curve, 
traced  in  the  figure  A  B  C  D,  and  for  general  pur- 
poses this  exposition  of  the  phenomena  seemed  entirely 
satisfactory.  It  is  true  that  it  only  accounted  for  the 
movement  from  east  to  west,  or  in  longitude,  while  the 
motion  north  and  south  of  the  earth's  orbit,  or  in  lati- 
tude, was  accounted  for  by  supposing  the  plane  of  the 
epicycle  to  vibrate  or  rock  up  and  down,  or  right  and  left 
of  the  plane  of  the  ecliptic,  while  its  center  moved  uni- 
formly round  in  the  great  circle  constituting  the  orbit  of 
the  planet. 

So  long  as  observation  was  so  defective  as  to  yield  but 
rough  places  of  the  heavenly  bodies,  the  deviations  from 
the  path  marked  out  by  the  theory  of  epicycles  escaped 
detection.  The  erection  of  the  great  observatory  of 
Uraniberg,  by  the  celebrated  astronomer  Tycho  Brahe, 
and  the  furnishing  it  with  instruments  of  superior  deli- 
cacy, introduced  a  new  era  in  the  history  of  astronomical 
observation.  The  instruments  employed  by  Copernicus 


M  A  K  S  .  105 

were  incapable  of  giving  the  place  of  a  star  or  planet  with 
a  precision  such  as  to  avoid  errors  amounting  to  even  the 
half  of  one  degree,  or  an  amount  of  space  equal  to  the 
sun's  apparent  diameter.  The  instruments  employed  by 
Tycho  reduced  the  errors  of  observation  from  fractions 
of  degrees  to  fractions  of  minutes  of  arc,  and  when  thus 
critically  examined,  the  planets,  as  well  as  the  sun  and 
moon,  presented  anomalies  of  motion,  requiring  to  ac- 
count for  them  a  large  accumuktion  of  complexity  in 
the  celestial  machinery.  Such  was  the  condition  of 
theoretic  and  practical  astronomy  at  the  era  inaugurated 
by  the  appearance  of  the  celebrated  Kepler.  This  dis- 
tinguished astronomer  early  became  a  devoted  advocate 
of  the  Copernican  system  of  the  universe,  adopting  not 
only  the  central  position  of  the  sun,  but  also  the  ancient 
doctrine  of  uniform  circular  motion,  and  the  theory  of 
epicycles.  The  investigations  of  Kepler  on  the  motions 
of  the  planet  Mars  commenced  after  joining  Tycho  at 
Uraniberg,  in  1603,  and,  based  upon  the  accurate  observa- 
tions of  this  later  astronomer,  finally  led  to  the  overthrow 
of  the  old  theory  of  epicycles  and  circular  motion,  intro- 
duced the  true  figure  of  the  planetary  orbits,  and  with 
the  elliptical  theory  of  planetary  motion,  commenced  the 
dawn  of  that  brighter  day  of  modern  science,  which  in 
our  age  sheds  its  light  upon  the  world. 

The  history  of  the  great  discoveries  of  Kepler  presents 
one  of  the  most  extraordinary  chapters  in  the  science  of 
astronomy.  It  must  be  remembered  that  the  doctrine  of 
circular  motion,  at  once  so  beautiful  and  simple,  had  held 
its  sway  over  the  human  mind  for  more  than  two  thou- 
sand years.  Such,  indeed,  was  its  power  of  fascination 
that  even  the  bold  and  independent  mind  of  Copernicus 
could  not  break  away  from  its  sway.  When  Kepler 


106  MARS. 

commenced  his  examination  of  the  movements  of  Mars  it 
was  under  the  full  and  firm  conviction  that  the  theory  of 
circles  and  epicycles  was  unquestionably  true.  His  task, 
then,  was  simply  to  frame  a  combination  such  as  would 
account  for  the  new  anomalies  in  the  motions  of  Mars 
discovered  by  the  refined  observations  of  Tycho.  The 
amount  of  industry,  perseverance,  sagacity,  and  invent- 
ive genius  displayed  by  Kepler  in  this  great  effort  is 
Xinparalleled  in  the  history  of  astronomical  discovery. 
His  plan  of  operation  was  admirably  laid,  and  if  fully 
and  faithfully  carried  out,  could  not  fail,  in  the  end,  to 
exhaust  the  subject,  and  to  prove  at  least  the  great  nega- 
tive truth,  that  no  combination  of  circles  and  epicycles 
could  by  any  possibility  truly  represent  the  exact  move- 
ments of  this  flying  world.  It  is  useless  to  enumerate 
the  different  hypotheses  employed  by  Kepler.  They 
were  no  less  than  nineteen  in  number,  each  of  which 
was  examined  with  the  most  laborious  care,  and  each  of 
which,  in  succession,  he  was  compelled  to  reject.  Having 
adopted  an  hypothesis,  he  computed  what  ought  to  be  the 
visible  positions  of  the  planet  Mars,  as  seen  from  the 
earth,  throughout  its  entire  revolution.  He  compared 
these  computed  pla,ces  or  positions  with  the  observed 
places,  or  those  actually  occupied  by  the  planet,  and 
finding  a  discrepancy  between  the  two,  his  hypothesis 
was  thus  shown  to  be  false  and  defective,  and  must  neces- 
sarily be  rejected. 

It  is  curious  to  note  the  limits  of  accuracy  in  the  ob- 
served places  of  the  planet,  upon  which  Kepler  relied  with 
so  much  confidence  in  this  bold  investigation.  Many  of 
the  various  hypotheses  which  he  worked  up  and  applied 
with  so  much  diligence,  enabled  him  to  follow  the  planet 
in  its  entire  revolution  around  the  sun,  with  discrepancies 


MARS.  107 

between  observation  and  computation  not  exceeding  the 
lenth  part  of  the  moon's  diameter.  Indeed,  the  whole 
error  in  the  computed  place  of  Mars,  when  compared 
with  its  observed  place,  when  Kepler  commenced  the 
problem,  did  not  exceed  eight  minutes  of  arc,  or  about 
one-fourth  of  the  moon's  apparent  diameter,  and  yet  upon 
this  slender  basis  this  wonderful  man  declared  that  he 
would  reconstruct  the  entire  science  of  the  heavens. 

Having  thus  framed  one  hypothesis  after  another,  each 
of  which  was  in  its  fa^n  rigorously  computed,  applied 
and  rejected,  this  exhaustive  process  finally  brought 
Kepler  to  the  conclusion  that  no  combination  of  circles, 
with  circular  motion,  could  render  a  satisfactory  account 
of  the  anomalies  presented  in  the  revolution  of  Mars ; 
and  he  thus  rose  to  the  grand  truth,  that  the  circle,  with 
all  its  beauty,  simplicity,  and  fascination,  must  be  banished 
from  the  heavens. 

The  demonstration  of  this  great  negative  truth  was  a 
necessary  preliminary  to  the  discovery  of  the  true  orbit 
in  which  Mars  performed  his  revolution  around  the  sun. 
Complexity  having  been  exhausted  in  the  combination 
of  circles  without  success,  Kepler  determined  to  return 
to  primitive  simplicity  and  endeavor  to  find  some  one 
curve  which  might  prove  to  be  that  described  by  the 
planet.  In  tracing  up  the  movement  of  Mars,  as  we 
have  seen,  the  figure  of  the  true  orbit  was  evidently  an 
oval,  and  among  ovals  there  is  a  curve  known  to  geome* 
tricians  by  the  name  of  the  ellipse.  This  curve  is  sym- 
metrical in  form,  and  enjoys  some  peculiar  properties 
which  we  will  exhibit  to  the  eye. 

The  line  A  B  is  called  the  major  axis,  and  is  the 
longest  line  which  can  be  drawn  inside  the  curve.  It 
passes  from  one  vertex  A  to  the  other  vertex  at  B,  and 


108 


M  AKS. 


the  semi-ellipse  A  D  B  is  such  that  if  turned  round  the 
axis  A  B,  it  would  fall  on,  and  exactly  coincide  with  the 
semi-ellipse,  A  C  B.  The  line  C  D  is  called  the  minor 
axis,  and  is  the  shortest  line  which  can  be  drawn  in  the 
ellipse.  This  line  divides  the  figure  into  two  equal  por- 
tions, exactly  symmetrical. 


The  point  L  is  called  the  center  of  the  ellipse,  and  di- 
vides all  the  lines  drawn  through  it  and  terminating  in 
the  curve  into  two  equal  parts.  But  there  are  two 
points,  0  and  0',  called  the  /oci,  which  enjoy  very  pe- 
culiar properties.  If  from  C  as  a  center,  and  with  a 
radius  equal  to  A  L,  the  semi-major  axis,  we  describe  an 
arc,  it  will  cut  the  major  axis  in  0  and  (X,  the  two  foci. 
Now,  in  case  we  assume  any  point  on  the  curve  as  P, 
and  join  it  with  0  and  O',  the  sum  of  these  lines,  0  P 
and  0'  P,  will  be  equal  to  the  major  axis,  A  B. 

Such  are  the  distinguishing  properties  of  the  curve, 
which  holds  the  next  rank  in  order  of  beauty,  simplicity, 
and  regularity,  after  the  circle.  While  the  circle  has 
one  central  point,  from  which  all  lines  drawn  to  the  curve 
ire  equal,  the  ellipse  has  two  foci,  from  which  lines 


MARS. 


109 


drawn  to  the  same  point  on  the  curve,  when  added  to- 
gether, are  equal  in  length  to  the  major  axis.  When 
the  major  axis  of  the  ellipse  is  assumed  as  the  diameter 
of  a  circle,  the  circumference  will  wholly  inclose  the 
ellipse.  When  the  minor  axis  is  assumed  as  the  diame- 
ter, the  circumference  will  lie  wholly  within  the  ellipse. 
When  the  foci,  0  and  0',  are  very  near  the  center,  then 
these  circles,  and  the  ellipse  lying  between  them,  are  very 
close  to  each  other. 

When  Kepler  was  compelled  to  abandon  the  circle  and 
circular  motion  as  a  means  of  representing  the  planetary 
revolutions,  he  adopted  the  ellipse  as  the  probable  form 
of  the  orbits  of  these  revolving  worlds,  and  made  an 
especial  effort  to  apply  this  new  figure  to  a  solution  of 
the  mysteries  which  still  enveloped  the  motions  of  Mars. 
But  here  a  new  difficulty  presented  itself.  In  the  circu- 
lar orbits  and  epicycles  a  uniform  motion  was  always 
accepted,  but  in  the  ellipse,  every  point  of  which  is  at 
unequal  distances  from  the  focus,  some  law  of  velocity 
had  to  be  discovered  to  render  it  possible  to  compute  the 
planet's  place,  even  after  the  axis  of  the  ellipse  had 
been  determined.  Here  again  was  opened  up  to  the 
mind  of  the  laborious  philosopher  a  wide  field  of  investi- 
gation. Many  were  the  hypotheses  which  he  framed, 
computed,  applied  and  rejected,  but  finally  fixing  the 
sun  in  the  focus  of  the  assumed  elliptic  orbit,  and  as- 
suming that  the  line  drawn  from  the  sun's  center  to 
the  planet  would  sweep  over  equal  amounts  of  area  in 
equal  times ,  he, computed  the  places  of  Mars  through  an 
entire  revolution.  These  newly  computed  places  were 
now  compared  with  those  actually  filled  by  the  revolving 
world,  and  Kepler  found  to  his  infinite  delight  that  the 
planet  swept  over  the  precise  track  which  his  hypothesis 


110  MARS. 

had  enabled  him  to  predict,  and  with  an  exultation  of 
victorious  triumph  to  which  the  history  of  pure  thought 
furnishes  few  parallels,  Kepler  announced  to  the  world 
his  two  first  laws  of  planetary  motion,  which  may  be 
given  as  follows :  - 

1.  Every  planet  revolves  in  an  elliptical  orbit  about 
the  sun,  which  occupies  the  focus. 

2.  The  velocity  of  the  planet  on  every  point  of  its 
orbit  is  such  that  the  line  drawn  from  the  sun  to  the 
planet  will  sweep  over  equal  areas  in  equal  times. 

At  the  time  Kepler  lived,  human  genius  could  not 
have  won  a  grander  triumph,  for  it  was  not  only  a 
triumph  over  nature,  which  compelled  her  to  render  up 
her  inscrutable  secrets,  but  a  triumph  which  for  ever 
freed  the  mind  from  the  iron  sway  of  the  schools,  and 
from  the  prejudices  which  had  become  venerable  with  the 
lapse  of  more  than  twenty  centuries  of  unyielding  power. 
No  grander  emotions  ever  swelled  the  human  heart  than 
those  which  Kepler  experienced  when,  tracing  this  fiery 
world  through  his  sweep  among  the  fixed  stars,  he  found 
he  had  truly  and  firmly  bound  his  now  captive  planet  in 
chains  of  adamant,  from  which  in  all  future  ages  it  couid 
never  escape,  having  fixed  for  all  time  the  figure  of  the 
orbit  and  the  law  of  its  orbital  velocity.  This  extended 
notice  is  due  to  the  well  merited  fame  of  Kepler,  as  well 
as  to  the  grandeur  of  the  laws  discovered. 

The  elliptical  theory,  now  successfully  applied  to  the 
planet  Mars,  was  extended  rapidly  to  Mercury,  to  the 
moon,  and  in  order  to  all  the  known  planets.  We  shall 
hereafter,  in  our  treatment  of  the  planets,  adopt  the  el- 
liptical theory,  and  to  render  our  language  entirely  intel- 
ligible, will  proceed  to  explain  what  is  meant  by  the  ele- 
ments of  the  orbit  of  a  planet. 


MARS.  Ill 

To  determine  the  magnitude  of  any  ellipse,  we  must 
know  the  longer  and  shorter  axis,  or  the  longer  axis  and 
the  distance  from  the  center  to  the  focus,  called  the  eccen- 
tricity. 

To  determine  the  position  of  the  plane  of  an  ellipse,  we 
must  know  the  position  of  the  line  of  its  intersection  with 
a  given  plane,  (usually  the  ecliptic)  called  the  line  of 
nodes,  and  also  the  angle  of  inclination  with  this  fixed 
plane. 

To  determine  the  position  of  the  elliptical  orbit  in  its 
own  plane,  we  must'  know  the  position  of  the  vertex,  or 
extremity  of  the  major  axis,  called  the  perihelion. 

And  finally,  to  trace  the  planet  after  all  these  matters 
shall  be  known  as  to  its  orbit,  we  must  know  its  place 
or  position  in  its  orbit  at  a  given  moment  of  time,  and 
its  period  of  revolution. 

Now,  every  plane  of  every  planetary  orbit  passes 
through  the  sun's  center. 

Every  longer  axis  of  every  planetary  orbit  passes 
through  the  sun's  center,  and  every  line  of  nodes  of  all 
the  planetary  orbits  passes  through  the  sun's  center. 
Thus  we  have  one  point  of  every  axis,  line  of  nodes,  and 
plane  of  every  orbit  of  the  primary  planets. 

To  obtain  the  longer  axis  we  have  only  to  measure  the 
planet's  distance  from  the  sun  when  in  aphelion  and  in 
perihelion.  These  distances  added  together  make  the 
longer  axis  of  the  orbit.  The  perihelion  distance  being 
known,  we  readily  obtain  the  eccentricity,  hence  the 
shorter  axis,  and  from  these  the  entire  ellipse  in  magni- 
tude. The  point  at  which  a  planet  passes  from  north  to 
south  of  the  ecliptic  is  one  point  in  its  line  of  nodes,  the 
sun's  center  is  another,  uid  these  determine  the  direc- 
tion of  the  line  of  nodes.  The  inclination  of  plane  of  the 


112  MARS. 

planet's  orbit  to  the  ecliptic  is  measured  by  the  angle 
formed  between  a  line  drawn  from  the  sun's  center  per- 
pendicular to  the  line  of  nodes  in  the  plane  of  the  eclip- 
tic, and  one  perpendicular  to  the  same  line  at  the  same 
point,  but  lying  in  the  plane  of  the  planet's  orbit.  The 
elevation  therefore  of  the  planet  above  the  ecliptic,  when 
90°  degrees  from  the  node,  will  be  the  angle  of  inclina- 
tion. Having  the  line  of  nodes  and  inclination,  we  can 
draw  the  plane.  Having  the  perihelion  point,  longer 
axis  and  eccentricity,  we  can  construct  and  locate 
the  elliptic  orbit,  and  having  the  moment  of  perihel- 
ion passage,  we  can  trace  the  planet  in  its  future  move- 
ments. 

The  elliptical  theory  being  adopted  and  extended  to  all 
the  known  planets  successfully,  it  became  manifest  to 
the  searching  genius  of  Kepler  that  there  existed  too 
many  common  points  of  resemblance  between  these  re- 
volving orbs  not  to  involve  some  common  bond  which 
united  them  into  a  scheme  of  mutual  dependence.  They 
all  revolved  in  elliptical  orbits.  These  orbits  had  one 
common  focus,  the  sun.  The  lines  of  nodes  and  princi- 
pal axes  intersected  in  the  sun.  They  all  obeyed  the 
same  law  in  their  revolution  in  their  orbits,  and  Kepler 
now  ~iidertook  the  task,  almost  hopeless  in  its  character, 
of  discovering  some  bond  of  union  which  might  reduce  a 
multitude  of  now  isolated  worlds  to  an  orderly  and  de- 
pendent system. 

This  problem  occupied  the  mind  of  Kepler  for  no  less 
than  nineteen  years.  He  examined  carefully  all  the  ele- 
ments of  the  planetary  orbits,  and  finally  selected  the 
mean  distances  and  periodic  times  as  the  objects  of  his 
special  investigation.  He  found  that  the  periods  of  re- 
volution increased  as  the  planet  was  more  remote  from 


MARS.,  113 

the  sun,  but  certainly  not  in  the  exact  ratio  of  the  dis- 
tance.    Thus — 

The  mean  distance  of  the  earth  is        .        .  95,000,000  of  miles. 

Its  period  of  revolution,        .        .        .  365  J  days. 

Mean  distance  of  Mars,        ....  142,000,000  of  miles. 

Period  of  revolution, 687  days. 

Tn  case  the  distances  and  periodic  times  were  exactly 
proportional,  we  should  have  -VV-— IH-  But  -W-=l-5 
nearly,  while  ||J=1.9  nearly.  Finding  that  no  simple 
proportion  existed  between  these  quantities,  Kepler  broke 
away  from  the  ratios  of  geometry,  which  up  to  his  own 
era  had  almost  exclusively  been  employed  in  all  astrono- 
mical investigations,  and  conceived  the  idea  that  the  hid- 
den secret  might  be  found  in  proportions  existing  between 
some  powers  of  the  quantities  under  consideration.  He 
first  tried  the  squares,  or  simple  products  of  the  quanti- 
ties by  themselves.  Here  he  was  again  unsuccessful. 
He  now  rose  yet  higher,  and  examined  the  relations  of 
the  cubes  of  the  periods  and  distances.  But  no  propor- 
tion was  found  to  exist  among  these  third  powers.  At 
length  he  was  led  by  some  influence,  he  knew  not  what,  as 
he  says,  to  try  the  relation  between  the  squares  of  the  peri; 
ods  and  the  cubes  of  the  distances,  thus,  ||f  x  f  |J,  and 
j_Y_  x  j_4_3_  x  _i_4_2_ .  an(j  here  }av  the  grand  secret,  for  if  any 
one  will  perform  the  operations  above  indicated,  and  square 
the  periods  of  revolution,  and  cube  the  mean  distances, 
he  will  find  the  above  quantities  to  be  equal  to  each  other, 
or,  in  other  language,  he  will  find  the  squares  of  the 
periodic  times  exactly  proportional  to  the  cubes  of  tlie 
mean  distances. 

This  is  called  the  third  law  of  Kepler,  and  is  perhaps 
the  grandest  and  most  important  of  all  his  wonderful  dis- 
coveries. Through  its  power  the  worlds  are  all  linked 


114  MARS. 

together.  The  satellites  of  the  planets  revolve  in  obedi- 
ence to  its  swa,y,  and  even  those  extraordinary  objects, 
the  revolving  double  stars,  are  subjected  to  the  same  con- 
trolling law.  It  resolves  at  once  the  most  difficult  pro- 
blems involved  in  the  solar  system,  .affording  a  simple 
method  of  determining  the  mean  distances  of  all  the 
planets,  by  measuring  the  mean  distance  of  any  one 
planet,  and  by  observing  the  periods  of  revolution. 

As  we  have  already  seen,  the  periodic  times  are  read- 
ily determined  from  noting  the  days  and  fractions  of  days 
which  elapse  from  the  planet's  passage  through  its  node 
until  it  returns  to  the  same  node  again.  This,  in  case 
the  line  of  nodes  remained  absolutely  fixed,  would  give 
the  time  of  revolution  precisely,  and  a  slight  correction 
suffices  to  correct  the  error  due  to  the.  movement  of  the 
nodes.  The  determination  of  the  mean  distance  of  the 
earth,  then,  becomes  the  key  to  a  knowledge  of  all  the 
planetary  distances,  from  which  flows  the  absolute  magni- 
tudes of  the  planets  and  their  densities. 

It  is  not,  then,  surprising  that  Kepler,  seeing  the 
grandeur  of  the  consequences  flowing  from  the  great  dis- 
covery, should  have  given  utterance  to  his  feelings  in 
language  of  the  most  lofty  enthusiasm. 

With  the  knowledge  of  the.  three  laws  discovered  by 
Kepler  modern  astronomy  commenced  a  career  of  won- 
derful success.  We  shall  find,  hereafter,  that  even  these 
great  laws  of  Kepler  are  but  corollaries  to  a  higher  law 
yet  remaining  to  be  developed,  but  we  prafer  to  follow 
out  the  order  of  examination  and  development  already 
commenced. 

We  resume  our  discussion  of  the  planet  under  exami- 
nation. The  changes  in  the  apparent  diameter  of  Mars 
must,  of  course,  be  very  great  When  in  opposition  to 


MARS.  AUG.  30.  8  H.  55  M    1845 


MARS, CINCINNATI  OBSERVATORY 
AUG.  5  T.H  1845. 


MAES.  115 

the  sun,  or  on  a  lino  joining  the  sun  and  earth,  Mars  is 
only  forty-seven  millions  of  miles  from  our  planet,  while, 
on  reaching  his  conjunction  with  the  sun,  this  distance  is 
increased* by  the  entire  diameter  of  the  earth's  orbit,  or 
196  millions  of  miles.  When  in  opposition  Mars  shines 
with  great  splendor,  presenting  to  the  eye,  as  shown  by 
the  telescope,  a  large  and  well-defined  disk,  with  a  sur- 
fatv.  Distinctly  marked  with  permanent  outlines  of  what 
have  been  conjectured  to  be  continents  and  oceans.  The 
polar  regions  are  distinguished  by  zones  of  brilliant  white 
light,  which,  in  consequence  of  their  disappearance  un- 
der the  heat  of  summer,  and  their  reappearance  as  the 
winter  comes  on,  have  been  considered  as  due  to  snow 
and  ice.  I  have  examined  these  snow  zones  with  the 
great  refractor  of  the  Cincinnati  Observatory,  under 
peculiarly  favorable  circumstancs.  To  illustrate  the 
mode  of  observation  employed  in  the  determination  of  the 
period  of  rotation  of  Mars  on  its  axis,  and  the  power  of 
the  telescope  in  the  revelation  of  the  physical  constitu- 
tion of  this  planet,  I  append  some  account  of  Maedler's 
observations,  made  in  1830,  and  also  of  those  made  at  the 
Cincinnati  Observatory  in  1845  : — 

The  last  opposition  of  Mars,  which  occurred  on  the 
20th  August,  1845,  furnished  a  fine  opportunity  for  the 
inspection  of  the  irregularities  of  its  surface.  When  in 
opposition  the  planet  rises  as  the  sun  sets,  and.  the  earth 
and  planet  are  in  a  straight  line,  which,  by  being  pro- 
longed, passes  through  the  sun.  As  the  orbit  of  Mars 
incloses  that  of  the  earth,  it  will  be  seen  from  a  little  re- 
flection that  when  Mars  is  in  opposition  it  is  nearer  to 
the  earth  than  at  any  other  time,  nearer  than  when  in 
conjunction  by  the  entire  diameter  of  the  earth's  orbit, 
or  190  millions  of  miles.  In  case  the  orbits  of  Mars  and 


116  MARS. 

the  earth  were  exact  circles,  the  distance  between  the  two 
planets  at  every  opposition  would  be  the  same,  but  the 
elliptic  figure  of  the  orbits  occasions  a  considerable  varia- 
tion in  this  distance,  and  the  least  distance  possible  be- 
tween the  earth  and  Mars  will  be  when  an  opposition  oc- 
curs at  the  time  that  the  earth  is  furthest  from  the  sun 
and  Mars  nearest  to  the  sun.  Such  was  approximately 
the  relative  positions  of  the  planets  in  1845,  and  their 
distance  was  then  less  than  it  can  be  again  for  nearly  15 
years.  During  the  opposition  which  occurred  in  1830, 
the  earth  and  Mars  held  nearly  the  same  relative  posi- 
tions. The  planet  was  observed  by  Dr.  Maedler,  the  pres- 
ent distinguished  Director  of  the  Imperial  Observatory  at 
Dorpat,  Russia,  assisted  by  Mr.  Beer.  I  have  translated 
the  following  notices  from  Schumacher's  journal : — 

"  The  opposition  of  Mars  which  occurred  in  the  month 
of  September  of  this  year  (1830),  and  at  which  time  this 
planet  approached  nearer  the  earth  than  it  will  again  for 
15  years,  induced  us  to  observe  the  planet  as  often  as  the 
clouds  would  permit,  in  order  to  determine  the  position 
and  figure  of  its  spots ;  their  possible  physical  changes, 
and  especially  the  time  of  revolution  on  its  axis.  The 
telescope  employed  was  a  Franenhofer  Refractor,  4^  feet 
focus. 

"  The  opposition  occurred  on  the  19th  September,  and 
the  nearest  approach  to  the  earth  (0,384)  on  the  14th  of 
the  same  month.  In  all  succeeding  oppositions  up  to 
1845,  this  distance  amounts  to  0.5,  and  even  up  to  0.65 
(the  unit  being  the  mean  distance  of  the  earth  from  the 
sun).  On  account  of  the  accurate  definition  of  the  instru- 
ment, we  were  able  to  employ  a  power  of  300  generally, 
and  never  less  than  185.  With  low  magnifying  powers, 
the  greatest  diameter  was  determined  to  be  a  little  less 


MAES.  117 

than  22".      Our  observations  extended  from  the  20th 

I  September  to  the  20th  October,  during  which  time  17 

!  nights,  more  or  less  favorable,  occurred,  and  all  sides  of 

Mars  came  into  view.     Thirty-five  drawings  were  exe- 

I  cuted.     It  was  not  thought  advisable  to  apply  a  microme- 

i  ter,  as  the  thickness  of  the  lines  would  have  produced 

greater  errors  in  such  minute  measures  than  those  arising 

from  a  careful  estimation  by  the  eye.      The  drawings 

were   invariably   made  with   the   aid   of  the  telescope. 

Commonly  a  little  delay  was  had,  till  the  undetermined 

figure  of  theispots  visible  at  the  first  glance  separated 

themselves  (to  the  eye)  into  distinct  portions. 

*  ****** 

"  On  the  10th  September  a  spot  was  seen  so  sharp 
and  well  defined,  and  so  near  the  center  of  the  planet, 
that  it  was  selected  to  determine  the  period  of  rotation. 
On  the  14th  September  it  retrograded  from  the  eastern 
hemisphere,  through  the  center  to  the  western  hemis- 
phere, in  the  course  of  three  hours.  Its  figure  un- 
altered during  four  days,  and  its  regularity  as  to  rota- 
tion left  no  doubt  of  its  identity  and  permanence. 

"  In  the  course  of  2}  hours  Mars  exhibited  an  entirely 
different  appearance.  The  spot  (already  alluded  to) 
was  near  the  western  disk  of  the  planet.  On  the  16th  it 
was  again  observed,  and  the  period  of  revolution  de- 
duced. It  was  invisible  up  to  the  middle  of  October,  ap- 
pearing only  in  the  day  time  on  the  side  of  the  planet 
next  to  the  earth.  It  was  first  observed  again  on  the 
19th  October,  and  the  disk  of  Mars  showed  itself  with 
uncommon  sharpness.  On  the  southern  border  of  the 
principal  spot  two  red  spots  were  seen,  resembling  a 
ruddy  sky  on  the  earth.  They  appeared  fainter  an 
hour  after,  and  although  they  again  seemed  brighter 


118  MARS. 

they  were  never  again  seen  red.  We  also  observed  a 
faint  spot  near  the  principal  one,  which  was  never  after 
visible. 

##*#*#« 

"  The  observations  from  the  26th  September  to  the 
5th  October  showed  to  us  some  very  dark  spots,  which 
in  zone-formed  extensions  showed  a  strong  contrast  to 
the  brightly  illuminated  surfaces  free  from  spots.  A 
fragment  of  one  of  these  spots  was  at  the  north  end  dis- 
tinct and  broad,  while  at  the  south  end  it  was  so  small 
as  to  be  seen  with  difficulty.  Between  the  pole  and  the 
principal  spot,  there  was  seen  a  broad  stripe,  of  less 
shade,  while  the  northern  hemisphere  was  almost  en- 
tirely free  from  spots.  Bad  weather  interrupted  the  ob- 
servations from  the  5th  to  the  12th  October. 

"  On  the  13th,  a  spot  appeared  for  the  first  time 
again,  but  so  near  the  western  disk  that  we  recognized 
its  return  only  on  the  14th. 

"  More  accurate  observations  were  had  on  the  19th 
and  20th  October,  when  this  spot  passed  the  -middle  of 
Mars,  which  movement  was  observed  with  all  accuracy, 
and  hence  a  new  determination  of  the  period  of  revolu- 
tion. Computation  gave  the  magnitude  of  the  invisible 
part  of  Mars  on  the  13th  October=0.06,  on  the  20th, 
0.08,  of  the  radius  of  Mars. 

"  From  the  beginning  of  the  observations  there  was 
seen  at  the  south  pole,  always  with  great  distinctness,  a 
white,  glittering,  well  defined  spot,  which  has  long  been 
observed,  and  is  called  the  '  snow  zone?  During  the 
observations  it  continually  diminished  up  to  the  5th  of 
October.  Here  an  increase  commenced,  yet  very  slow. 
On  the  10th  September  we  estimated  it,  =.110;  5th 
Oct.  =  .110,  and  20th  Oct  =.115  of  the  diameter  of  Mars. 


MAKS.  119 

"  In  case  we  adopt  Herschel's  determination  of  inclina- 
tion and  position  of  the  axis  of  Mars,  with  reference  to  its 
orbit,  the  south  pole  of  Mars  on  the  14th  of  April,  1830, 
must  have  had  its  equinox,  and  on  the  8th  September, 
its  summer  solstice.  The  smallest  diameter  of  the  '  snow 
zone  '  occurred  on  the  27th  day  after  the  summer  sol- 
stice, a  time  which  corresponds  to  the  last  half  of  July 
on  the  northern  hemisphere  of  the  earth,  at  which  time 
it  is  well  known  we  have  the  greatest  heat. 

"  Preceding  observers  in  oppositions,  where  the  pole 
flras  further  from  the  maximum  temperature,  have  seen 
the  '  snow  zone  '  much  larger,  although  nearly  all  regard 
it  as  changeable  in  size.  These  facts  seem  to  sustain  the 
hypothesis  of  a  covering  of  snow." 

As  a  further  confirmation  of  this  hypothesis,  we  sub- 
join the  following  computations,  by  the  same  persons. 
The  previous  determinations  of  the  elder  Hersohel  are 
taken  as  the  basis  of  the  calculations.  This  white  polar 
region  is  now  distinctly  visible,  and  seems  to  be  accounted 
for  in  no  other  way.  Comparing  the  various  seasons  in 
Mars,  Maedler  finds  as  follows  ;  — 


"Duration  of  Spring,  N.  Hemisphere,  .        .  191£  Mars'  days. 

"  Summer,         "  ...  180  " 

'"  *  Autumn,         "  ...  149J-          " 

"  Winter,  "  ...  147  " 

lt  Adding  spring  and  summer  together,  and  fall  and 
winter,  we  have  — 

"  Duration  of  Summer  in  N.  H.  to  S.  H.,     .    .        .    as  19  to  15 
"  Intensity  of  sun's  light  in  N.  H.  to  S.  H.,       .        .    as  20  to  29 

"  Uniting  these  two  proportions,  and  assuming  that 
heat  and  light  are  received  in  equal  ratios,  it  will  follow 
that  the  south  pole,  by  the  greater  intensity  of  solar  heat, 
is  more  than  compensated  for  the  shortness  of  its  sum- 


120  MARS. 

rner.  But  since  for  the  winter  the  proportion  of  20  to  29 
is  reversed,  so  will  the  winter  of  the  south  pole,  not  only 
on  account  of  longer  duration  of  cold,  but  also  from  its 
greater  intensity,  be  far  more  severe  than  in  the  north 
pole. 

"  Herewith  agree  the  facts  that  preceding  observers 
have  not  lost  sight  of  the  '  snow  zone '  of  the  south  pole, 
even  when  the  pole  became  invisible,  whence  it  follows 
that  it  must  extend  from  the  pole  45°  degrees  and  even 
further,  while  we,  under  like  circumstances,  could  not 
discover  any  such  appearance  on  the  north  side  of  Mars. 
On  the  contrary,  the  brightness  of  this  portion  was  exactly 
like  that  of  the  other  parts  of  the  disk." 

The  conclusions  reached  by  the  German  astronomers, 
as  above,  were  confirmed  in  the  fullest  manner  by  the 
observations  made  at  the  Cincinnati  Observatory  during 
the  opposition  of  1845.  I  will  here  record  some  singular 
phenomena  connected  with  the  "  snow  zone,"  which,  so  far 
as  I  know,  have  not  been  noticed  elsewhere. 

On  the  night  of  July  12th,  1845,  this  bright  polar 
spot  presented  an  appearance  never  exhibited  at  any  pre- 
ceding or  succeeding  observation.  In  the  very  center  of 
the  white  surface  was  a  dark  spot,  which  retained  its 
position  during  several  hours,  and  was  distinctly  seen  by 
two  friends,  who  passed  the  night  with  me  in  the  observa- 
tory. It  was  much  darker  and  better  defined  than  any 
spot  previously  or  subsequently  observed  here,  and,  in- 
deed, after  an  examination  of  more  than  eighty  drawings 
of  the  surface  of  this  planet  by  other  observers  at  previ- 
ous oppositions,  I  find  no  notice  of  a  dark  spot  ever  hav- 
ing been  seen  in  the  bright  snow  zone.  On  the  following 
evening  no  trace  of  a  dark  spot  was  to  be  seen,  and  it  has 
never  after  been  visible. 


MARS.  121 

Again,  on  the  evening  of  August  29th,  1845,  the  snow 
zone,  which  for  several  weeks  had  presented  a  regular 
outline,  nearly  circular  in  appearance,  was  found  to  be 
somewhat  flattened  at  the  under  part,  and  extended  east 
and  west  so  as  to  show  a  figure  like  a  rectangle,  with  its 
corners  rounded.  On  the  evening  of  the  30th  August  I 
observed,  for  the  first  time,  a  small  bright  spot,  nearly 
or  quite  round,  projecting  out  of  the  lower  side  of  the 
polar  spot  In  the  early  part  of  the  evening  the  small 
bright  spot  seemed  to  be  partly  buried  in  the  large  one, 
and  was  in  this  position  at  8h.  55m.,  when  the  draw- 
ing, No.  1,  was  made.  After  the  lapse  of  an  hour  or 
more,  my  attention  was  again  directed  to  the  planet,  when 
I  was  astonished  to  find  a  manifest  change  in  the  posi- 
tion of  this  small  bright  spot.  It  had  apparently  sepa- 
rated from  the  large  spot,  and  the  edges  of  the  two  were 
now  in  contact,  whereas  when  first  seen  they  overlapped 
by  an  amount  quite  equal  to  one-third  the  diameter  of 
the  small  spot.  On  the  following  evening  I  found  a  re- 
currence of  the  same  phenomena.  In  the  course  of  a  few 
days  the  small  spot  gradually  faded  from  the  sight  and 
was  not  seen  at  any  subsequent  observation.  Should 
flerschel's  hypothesis  be  admitted,  that  the  bright  zone 
is  produced  by  snow  and  ice  near  the  pole  of  the  planet 
analogous  to  what  is  known  to  exist  at  the  poles  of  the 
earth,  these  last  .changes  may  be  accounted  for,  by  sup- 
posing the  small  bright  spot  to  have  been  gradually 
dissipated  by  the  heat  of  the  sun's  rays. 

Its  apparent  projection  over  the  boundary  of  the  large 
snow  zone  may  have  been  merely  optical,  and  the  sepa- 
ration may  have  been  occasioned  by  seeing  the  two  ob- 
jects in  such  position  as  to  prevent  the  one  from  being 
projected  on  the  other.  Such  change  may  have  been 


122  MARS. 

produced  by  the  rotation  of  Mars  on  its  axis  in  the  space 
of  a  few  hours. 

To  determine  the  exact  period  of  rotation  of  Mars,  Sir 
William  Herschel  instituted  a  series  of  observations  in 
1777,  which  were  followed  by  others  during  the  opposi- 
tion of  1779.  From  the  first  series  an  approximate 
period  of  rotation  was  obtained,  and  by  uniting  the  ob- 
servations of  1777  and  those  of  1779,  and  using  24h. 
39m.  as  the  approximate  period  of  rotation,  Herschel 
made  a  further  correction,  and  fixed  the  rotation  at  24h. 
39m.  21.6s. 

Maedler's  determination,  in  1830,  gave,  for  a  final 
result,  24h.  37m.  10s.,  which,  in  1832,  was  corrected 
and  fixed  at  24h.  37m.  23.7s. 

In  1839  Maedler  reviewed  HerschePs  observations, 
from  whence  his  first  results  were  deduced,  and  discovered 
that  after  introducing  the  necessary  reduction,  the  dis- 
crepancy of  two  minutes  might  be  reduced  to  two  seconds, 
by  giving  to  Mars  one  more  rotation  on  its  axis,  between 
the  observations  of  1777  and  1779,  than  Herschel  had 
employed. 

In  1845,  when  Mars  again  occupied  the  same  relative 
position  that  it  had  done  in  1830,  it  was  too  far  south 
for  observation  at  Dorpat. 

By  combining  Maedler's  observation,  made  at  Berlin, 
1830,  September  14,  12h.  30m.,  with  one  made  at  the 
Cincinnati  Observatory,  1845,  August  30,  8h.  55m., 
making  the  corrections  due  to  geocentric  longitude, 
phase,  ami  aberration,  I  find  the  period  of  rotation  to  be 
24h.  37m.  20.6s.,  differing  by  only  two  seconds  from 
Maedler's  period  as  last  corrected. 

It  is  generally  believed  that  Mars  is  surrounded  by  an 
atmosphere  which  in  many  respects  resembles  our  own. 


MARS.  123 

In  case  this  be  true,  we  may  anticipate  the  existence  of 
belts  of  clouds,  and  occasional  cloudy  regions,  which 
would  modify  the  outline  of  the  great  tracts  of  sea  and 
land,  and  would  account  for  the  rapid  changes  which  are 
sometimes  noticed  in  the  surface  of  the  planet. 

The  axis  of  the  planet  is  inclined  to  its  orbit  (as  may 
readily  be  deduced  from  the  rotation  of  the  spots)  under 
an  angle  of  a  little  more  than  30°,  hence  the  variations 
of  climate  and  the  changes  of  season  in  Mars  will  not  be 
very  unhke  those  which  mark  the  condition  of  our  own 
planet.  Indeed,  there  are  many  strong  points  of  resem- 
blance in  the  planetary  features  of  the  earth  and  this 
neighboring  world.  The  planes  of  their  orbits  are  but 
little  inclined  to  each  other,  a  little  less  than  23.  Their 
years  are  not  widely  different  when  we  take  into  account 
the  vast  periods  which  distinguish  some  of  the  more  dis- 
tant planets. 

The  seasons  ought  to  be  nearly  alike,  and  the  length 
of  day  and  night,  as  determined  by  the  periods  of  rotation 
of  the  two  worlds,  is  nearly  the.same.  In  case  the  great 
geographical  outlines  are  alike,  and  seas  and  continents 
really  diversify  the  surface  of  Mars  with  an  atmosphere 
and  clouds,  the  two  worlds  bear  a  strong  resemblance  to 
each  other. 

The  actual  diameter  of  Mars  is  only  4,100  miles,  or  a 
little  more  than  half  the  diameter  of  our  earth,  while  its 
volume  is  not  much  greater  than  one- tenth  part  of  the 
TOlume  of  our  planet. 

To  the  inhabitants  of  Mars  (if  such  there  be)  the  earth 
and  moon  will  present  a  very  beautiful  pair  of  indissolu- 
bly  united  planets,  showing  all  the  phases  which  are 
presented  by  Mercury  and  Venus  to  our  eyes,  the  two 
worlds  never  parting  company,  and  always  remaining  at 


124  MAES. 

a  distance  of  about  one  quarter  of  one  degree,  or  about 
half  the  moon's  apparent  diameter. 

The  amount  of  heat  and  light  received  from  the  sun  by 
Mars  is  about  one  half  of  that  which  falls  on  the  earth ; 
and  in  case  the  planet  were  placed  under  the  identical 
circumstances  which  obtain  on  earth,  the  equatorial 
oceans  even  would  be  solid  ice.  This,  we  have  every  rea- 
son to  believe,  is  not  the  case,  and  hence  we  are  induced 
to  conclude,  as  in  other  cases,  that  the  light  and  heat  of 
the  sun  are  subjected  to  special  modifications,  by  atmo- 
spheric and  other  causes,  at  the  surfaces  of  each  of  the 
worlds  dependent  on  this  great  central  orb. 

The  reddish  tint  which  marks  the  light  of  Mars  has 
been  attributed  by  Sir  John  Herschel  to  the  prevailing 
color  of  its  soil,  while  he  considers  the  greenish  hue  of 
certain  tracts  to  distinguish  them  as  covered  with  water. 
This  is  all  pure  conjecture,  based  upon  analogy  and  de- 
rived from  our  knowledge  of  what  exists  in  our  own 
planet.  If  we  did  not  know  of  the  existence  of  seas  on 
the  earth,  we  could  never  conjecture  or  surmise  their 
existence  in  any  neighboring  world.  Under  what  modi- 
fication of  circumstances  sentient  beings  may  be  placed, 
who  inhabit  the  neighboring  worlds  it  is  vain  for  us  to 
imagine. 

It  would  be  most  incredible  to  assert,  as  some  have 
done,  that  our  planet,  so  small  and  insignificant  in  ita 
proportions  when  compared  with  other  planets  with  which 
it  is  allied,,  is  the  only  world  in  the  whole  universe  filled 
with  sentient,  rational,  and  intelligent  beings  capable  of 
comprehending  the  grand  mysteries  of  the  physical  uni- 
verse. 


CHAPTER  VI. 

THE  ASTEROIDS:  A  GROUP  OP  SMALL  PLANETS,  THH 
FIFTH  IN  THE  ORDER  OF  DISTANCE  FROM  THE  SUN. 


THE  INTERPLANETARY  SPACES.— KEPLER'S  SPECULATIONS.— GREAT  INTERVAL  BE- 
TWEEN MARS  AND  JUPITER.— BODE'S  EMPIRICAL  LAW.— CONVICTION  THAT  A 
PLANET  EXISTED  BETWEEN  MAES  AND  JUPITER.— CONGRESS  OF  ASTRONOMERS. 
—Aw  ASSOCIATION  ORGANIZED  TO  SEARCH  FOR  THE  PLANET.— DISCOTEBT  o» 
CERES.— LOST  IN  THE  SOLAR  BEAMS.— REDISCOVERED  BY  GAUSS.— THE  NEW 
ORDER  DISTURBED  BY  THE  DISCOVERY  OF  PALLAS.— OLLER'S  HYPOTHESIS. — 
DISCOVERY  OF  JUNO  AND  VESTA.— THE  SEARCH  CEASES.— EENEWED  IN  1S45. 
—MANY  ASTEROIDS  DISCOVERED.— THEIR  MAGNITUDE,  SIZE,  AND  PROBABLE 
NUMBEB, 


THE  worlds  thus  far  examined  in  our  progress  outward 
from  the  sun  have  been  known  from  the  earliest  ages. 
Those  constituting  the  group  under  consideration,  called 
asteroids,  have  all  been  discovered  since  the  commence- 
ment of  the  present  century. 

The  circumstances  attending  the  discovery  of 

CERES,  d)  OF  THE  ASTEROIDS  are  replete  with  interest, 
and  demonstrate  the  power  of  the  conviction  in  the  human 
mind  that,  in  the  organization  of  the  physical  universe, 
some  systematic  plan  will  be-  found  to  prevail.  In  draw- 
ing to  a  scale  the  solar  scheme  of  planetary  orbits,  it  was 
readily  observed  that  the  distances  of  the  planets  from  the 
sun  increased  in  a  sort  of  regular  order  up  to  the  orbit 
of  Mars.  Here,  between  Mars  and  Jupiter,  there  was 
found  a  mighty  interval,  after  which  the  order  was  re- 
stored as  to  the  planets  beyond  the  orbit  of  Jupiter. 

As  early  as  the  beginning  of  the  seventeenth  century, 


126  THE      ASTEROIDS. 

Kepler,  whose  singular  genius  was  captivated  by  mystical 
numbers  and  curious  analogies,  conjectured  the  existence 
of  an  undiscovered  planet  in  this  great  space  which  in- 
tervened between  Mars  and  Jupiter.  The  thought  thus 
thrown  out  required  no  less  than  two  hundred  years  to 
take  root  and  yield  its  legitimate  fruit.  The  discovery 
of  a  planet  beyond  the  orbit  of  Saturn,  by  Sir  William 
Herschel,  in  1781,  greatly  strengthened  the  opinions 
based  on  the*  orderly  arrangement  of  the  interplanetary 
spaces ;  and  the  German  astronomer,  Bode,  by  the  dis- 
covery of  a  curious  relation,  which  seemed  to  control 
the  distances  of  the  planets,  gave  additional  force  and 
power  to  the  conjecture  of  Kepler.  This  law  is  a  very 
remarkable  one,  and  although  no  explanation  could  be 
given  of  it,  was  verified  in  so  many  instances  as  almost 
to  force  one  to  the  conclusion  that  it  must  be  a  law  of 
nature.  We  present  the  law  in  a  simple  form.  Write 
the  series- 

0,       3,         6,       12,       24,         48,       96,  &c. 
add    4        4          4          4          4  4          4,  &c. 

sum  4  7  10  16  28  52  100,  &c. 
Now,  if  ten  be  taken  to  represent  the  distance  of  the 
earth  from  the  sun,  the  other  terms  of  the  series  will 
represent  with  considerable  truth  the  distances  of  the 
other  planets,  as  we  will  readily  perceive,  thus : — 
Mercury.  Venus.  Earth.  Mars.  Jupiter.  Saturn.  Uranus. 

4         7         10      16        28       52      100      196 
The  true  distances  are  roughly  as  under  : — 
3.8      7.2      10      15.2  52      95.3    191.8 

It  is  thus  seen  that  the  actual  distances  of  the  planets 
agree  in  a  most  remarkable  manner  with  those  obtained 


THE     ASTEROIDS.  127 

by  the  application  of  Bode's  Law,  and  as  no  planet  was 
yet  known  to  fill  the  distance  (28)  between  Mars  and 
Jupiter,  it  required  very  little  devotion  to  the  analogies 
of  nature  to  create  in  any  mind  a  firm  belief  in  the  ex- 
istence of  an  unknown  planet. 

The  German  astronomers,  at  the  close  of  the  last  cen- 
tury, took  up  the  matter  with  earnest  enthusiasm,  and  in 
the  year  1800  a  congress  or  convention  of  astronomers 
was  assembled  at  Lilienthal,  of  which  M.  Shroeter  was 
elected  president,  and  Baron  De  Zach  perpetual  secre- 
tary. It  was  agreed  to  commence  a  systematic  search 
for  the  unknown  planet,  by  dividing  the  belt  of  the 
heavens  near  the  sun's  path,  called  the  zodiac  (and  within 
whose  limits  all  the  planetary  orbits  are  confined),  among 
twenty-four  astronomers,  who  with  their  telescopes  should 
search  for  the  object  in  question. 

It  was  manifest  that  the  unknown  planet  must  be 
very  small,  too  small  to  be  visible  to  the  naked  eye, 
otherwise  its  discovery  must  have  been  long  since  accom- 
plished. It  might,  however,  prove  to  be  large  enough  to 
exhibit  a  planetary  disk  in  the  telescope,  in  which  event 
a  simple  search  was  all  that  was  required.  If,  however, 
it  should  be  too  diminutive  to  show  a  well  defined  disk  in 
the  telescope,  then  another  method  of  examination  would 
be  required.  The  planet  could  only  be  detected  by  its 
motion  among  the  fixed  stars.  This,  indeed,  is  the  way 
in  which  all  the  old  planets  had  been  discovered ;  but 
while  the  naked  eye  takes  in  at  the  same  time  a  large 
portion  of  the  celestial  sphere,  the  telescope  is  extremely 
limited  in  \tefield  of  view,  rendering  the  search  labor- 
ious and  difficult.  Were  it  possible,  however,  to  make  an 
exact  chart  of  all  the  stars  in  a  given  region  of  the  heav- 
ens, to-night,  if  an  examination  on  to-morrow  night  of 


128  THE     ASTEROIDS. 

the  same  region  should  show  a  strange  star  among  those 
already  charted,  this  stranger  might  with  some  proba- 
bility he  assumed  to  be  a  planet. 

A  few  hours  of  patient  watching  would  show  whether 
it  was  in  motion,  and  a  few  nights  of  observation  would 
reveal  its  rate  of  motion. 

Such  was  the  mode  of  research  adopted  by  the  society 
of  planet-hunters.  The  system  thus  adopted  had  not 
been  pursued  but  a  few  months  when  a  most  signal  suc- 
cess crowned  the  effort.  On  the  night  of  the  1st  January, 
1801,  Piazzi,  of  Palermo,  in  Sicily,  observed  a  star  in 
the  constellation  Taurus,  which  he  suspected  to  be  a 
stranger.  On  the  following  night  (having  fixed  its  posi- 
tion anew  with  reference  to  the  surrounding  stars),  he 
found  it  had  changed  its  place  by  an  amount  so  large 
that  its  real  motion  could  not  be  doubted.  The  star 
was  found  to  be  retrograding,  or  moving  backward,  and 
this  continued  up  to  the  12th  January,  when  it  became 
stationary.  It  was  soon  after  lost  in  the  rays  of  the  sun, 
thus  becoming  invisible,  before  any  considerable  portion 
of  its  orbit  had  been  observed,  and  before  Piazzi  could 
communicate  his  discovery  to  any  member  of  the  society. 

Piazzi  not  considering  it  possible  that  a  planet  which 
had  remained  hidden  from  mortal  vision  from  its  crea- 
tion could  be  discovered  with  so  little  effort  as  had  thus 
far  been  put  forth,  conceived  that  the  moving  body  which 
he  had  discovered  was  a  comet,  but  the  intelligence  hav- 
ing been  communicated  to  the  society,  Bode  promptly 
pronounced  this  to  be  the  long  sought  planet,  an  opinion  in 
which  he  was  sustained  by  Olbers  and  Buckhardt,  Baron 
de  Zach,  and  Gauss,  and  I  know  not  by  how  many  other 
members  of  the  society. 

It  now  became  a  matter  of  the  deepest  interest  to  re- 


THE    ASTEROIDS.  129 

discover  this  stranger  after  its  emergence  from  the  sun's 
rays,  a  task  of  no  little  difficulty,  as  we  will  see  by  the 
slightest  reflection.  The  star  had  been  followed  through 
only  about  4°  of  its  orbit,  and  on  this  slender  basis  it 
seemed  almost  impossible  to  erect  a  superstructure  such 
as  might  conduct  the  astronomer  to  the  point  occupied  at 
any  given  time  by  this  almost  invisible  world.  We  shall 
see  hereafter  that  this  most  astonishing  feat  was  success- 
fully accomplished  by  the  German  mathematician  and 
astronomer,  Gauss,  then  quite  a  young  man,  and  who,  in 
this  early  effort,  gave  evidence  of  that  high  ability  for 
which  he  became  afterward  so  greatly  distinguished. 

Ceres  being  re-discovered,  and  closely  observed,  the 
data  were  soon  obtained  for  the  exact  computation  of  the 
elements  of  its  orbit,  when  it  was  found  to  occupy,  in 
the  planetary  system,  the  precise  position  which  had  been 
assigned  to  it  fifteen  years  before  by  Baron  de  Zach,  in 
accordance  with  the  indications  of  the  curious  empirical 
rule,  already  presented,  known  as  Bode's  law. 

The  harmony  of  the  system  was  thus  fully  established, 
the  missing  term  in  the  series  was  now  filled.  The  vast 
interplanetary  space  between  Mars  and  Jupiter  was  the 
real  locality  of  a  discovered  world,  whose  existence  had 
been  conjectured  by  Kepler  two  hundred  years  before, 
and  whose  discovery,  by  combined  systematic  and  scien- 
tific examination,  constituted  the  crowning  glory  of  the 
age.  True,  the  new  planet  was  exceedingly  small  when 
compared  with  any  of  the  old  planets,  yet  it  acknowledged 
obedience  to  the  great  laws  established  by  Kepler,  re- 
volving in  an  elliptical  orbit  of  very  considerable  eccen- 
tricity, and  sweeping  round  the  sun  in  a  period  of  about 
four  years  and  nine  months,  and  at  a  mean  distance 
of  about  263  millions  of  miles. 


130  THE     ASTEROIDS. 

The  telescope  yielded  but  little  information  as  to  the 
absolute  magnitude  and  condition  of  Ceres.  Its  diame- 
ter has  been  measured  by  various  astronomers  but  the 
results  are  so  discordant  that  but  little  confidence  is  to 
placed  in  them.  It  cannot,  probably,  exceed  1,000  miles, 
and  may  be  much  less.  It  is  supposed  to  be  surrounded 
by  an  extensive  atmosphere,  but  the  evidence  of  this  is 
not  very  reliable.  Under  favorable  circumstances,  and 
with  a  powerful  telescope,  a  disk  can  sometimes  be  seen, 
but  for  the  most  part  Ceres  presents  the  appearance  of  a 
star  of  about  the  eighth  magnitude. 

Such  was  the  condition  of  astronomy,  affording  to 
those  interested  cause  for  high  gratification  in  the  now 
known  orderly  distribution  of  the  planetary  orbs,  when 
an  announcement  was  made  which  was  received  with 
profound  astonishment,  as  it  at  once  introduced  con- 
fusion precisely  at  the  point  in  which  order  had  been  so 
lately  restored.  This  was  the  discovery  of  another  small 
planet,  by  Olbers  of  Bremen,  revolving  in  an  orbit  nearly 
equal  to  that  occupied  by  Ceres.  Computation  and 
observation  united  in  fixing,  beyond  doubt,  this  most 
extraordinary  discovery,  and  the  new  and  anomalous 
body  received  the  name  of  Pallas.  The  exact  elements 
of  the  orbit  of  Pallas  having  been  determined,  it  was 
found  that  a  very  near  approximation  to  equality  existed 
between  the  mean  distances  and  periods  of  Ceres  and 
Pallas,  as  we  find  below : — 

Ceres' period  of  revolution,    ....  1,682.125  days. 

Pallas'      "  " 1,686.510     " 

Ceres'  mean  distance, 262,960,000  miles. 

Pallas'  " 263,435,000      " 

Here  we  find  the  mean  distances  and  periods  so  nearly 
equal,  that  in  case  the  planes  of  the  orbits  of  the  two 


THE     ASTEROIDS.  131 

planets  had  chanced  to  coincide,  these  two  worlds  might 
travel  side  bj  side  for  a  long  while,  and  at  a  distance 
from  each  other  only  about  double  the  distance  separating 
the  earth  from  her  satellite.  The  distance  between  Mars 
and  Ceres  is  no  less  than  120  millions  of  miles.  The 
distance  from  Ceres  orbit  to  that  of  Jupiter  is  more 
than  280  millions  of  miles,  and  yet  here  are  two  planets 
which  may  approach  each  other  to  within  a  distance  less 
than  half  a  million  of  miles. 

It  is  true,  the  eccentricities  of  the  orbits  differ  greatly, 
and  the  inclinations  of  their  orbital  .planes  is  also  very 
great,  so  that  Pallas,  by  this  inclination,  is  carried  far 
beyond  the  limits  within  which  the  planetary  excursions 
north  and  south  of  the  ecliptic  had  been  previously  con- 
fined, yet  a  time  would  come  in  the  countless  revolutions 
of  these  remarkable  worlds  when  each  would  fill,  at  the 
same  time,  points  of  the  common  line  of  intersection  of 
their  orbital  planes,  and  these  two  points,  owing  to  the 
revolutions  of  the  perihelion,  might,  possibly,  at  some 
future  period,  come  to  coincide. 

In  case  these  speculations  were  within  the  limits  of  the 
probable,  and  if  it  were  permitted  to  anticipate  in  the 
future,  the  possible  collision  or  union  of  these  minute 
planets,  a  like  train  of  reasoning,  running  back  into  the 
past,  would  lead  to  the  conclusion  that  in  case  their  rev- 
olution had  been  in  progress  for  unnumbered  ages,  there 
was  a  time  in  the  past  when  these  two  independent  worlds 
might  have  occupied  the  same  point  in  space,  and  hence 
the  thought  that  possibly  they  were  fragments  of  some 
great  planet,  which,  by  the  power  of  some  tremendous 
internal  convulsion,  had  been  burst  into  many  separate 
fragments.  This  strange  hypothesis  was  first  propounded 
by  Dr.  Gibers,  and  has  met  with  more  or  less  favor  from 


132  THE     ASTEROIDS. 

succeeding  astronomers,  even  up  to  the  present  day,  as 
we  shall  see  hereafter. 

True  or  false,  it  soon  produced  very  positive  results, 
for  it  occasioned  a  renewal  of  the  research  which  had  been 
discontinued  after  the  discovery  of  Ceres,  and  in  a  few 
years  two  more  planets  were  added  to  the  list  of  asteroids. 
The  search  was  long  continued,  and  it  was  not  until  the 
end  of  fifteen  years  that  Gibers  and  his  associates  became 
satisfied  that  no  more  discoveries  could  be  expected  to 
reward  their  diligence.  Thus  it  became  a  received  doc- 
trine that  in  case  a  Jarge  planet  had  been  rent  asunder 
by  some  internal  explosive  power,  it  had  been  burst  into 
four  pieces,  and  that  no  other  fragments  existed  sufficiently 
large  to  be  detected  even  by  telescopic  power. 

This  opinion  prevailed  up  to  December,  1845,  when 
the  astronomical  world  was  somewhat  startled  by  the 
announcement  of  a  new  asteroid,  discovered  by  Henke, 
of  Dreisen.  This  event  awakened  attention  to  this  sub- 
ject, and  a  new  generation  of  observers  entered  the  field 
of  research,  whose  efforts  have  resulted  in  revealing  a 
large  group  of  small  planets,  of  which  no  less  than  fifty- 
five  have  already  been  discovered,  and  their  orbits  com- 
puted. 

The  theory  of  the  disruption  of  one  great  planet  as 
the  origin  of  the  asteroids  has  been  revived  and  exten- 
sively discussed,  but  thus  far  no  satisfactory  conclusion 
has  been  reached.  So  strangely  are  the  orbits  of  these 
bodies  related  to  each  other  that,  in  case  they  all  laid  on 
the  same  plane,  they  would  in  some  instances  intersect 
each  other,  exhibiting  relations  nowhere  else  found  in  the 
solar  system.  None  of  the  asteroids  are  visible  to  the  naked 
eye,  nor  are  they  distinguishable  from  the  stars  with  the 
telescope,  except'  under  the  most  favorable  circumstances. 


THE     ASTEROIDS.  133 

When  carefully  watched  some  of  them  exhibit  rapid 
changes  in  the  intensity  of  their  light,  sometimes  sud- 
denly increasing  in  brightness,  and  again  as  rapidly  fad 
ing  out.  These  changes  have  been  accounted  for  on  the 
supposition  that  these  worlds  are  indeed  angular  frag- 
ments, and  that,  rotating  on  an  axis,  they  sometimes 
present  large  reflective  surfaces,  and  again  angular 
points,  from  whence  but  a  small  amount  of  light  reaches 
the  earth. 

As  the  stars  of  the  smaller  magnitudes  are  becoming 
more  extensively  and  accurately  charted,  tlieir  places 
being  determined  with  great  precision,  we  may  antici- 
pate a  large  increase  in  the  number  of  known  asteroids 
during  the  remainder  of  the  current  century,  and  so 
forward  ;  for  if  so  great  a  multitude  has  already  been  re- 
vealed almost  without  effort,  and  nearly  ty  accident, 
what  must  be  the  result  when  a  systematic  scheme  of 
examination  shall  have  been  executed,  based  on  an  ac- 
curate knowledge  of  the  places  of  all  the  stars  down  to 
the  twelfth  magnitude  ?  We  have  just  ground  for  sup- 
posing that  there  are  thousands  of  these  little  worlds 
revolving  in  space. 


CHAPTER  VII. 

JTJPITER,  ATTENDED  BY  FOUR  MOONS,  THE  SIXTH  PLANET 
IN  THE  ORDER  OF   DISTANCE    FROM   THE  SUN. 


A.EO  OF  RETROGRADATION.— STATIONARY  POINT.— DISTANCE  OF  THE  PLANET  DE- 
TERMINED.—PERIODIC  TIME.— SYNODIOAL  REVOLUTION  GIVES  THE  SIDEREAL, 
—SURFACE  OF  JUPITER  AS  GIVEN  BY  THE  TELESCOPE.— PERIOD  OF  ROTATION. 
DIAMETER. — VOLUME. — MEAN  DISTANCE. — AMOUNT  OF  LIGHT  AND  HEAT. — 
FIGURE  OF  JUPITER.— EQUATORIAL  AND  POLAR  DIAMETERS.— DISCOVERY  OF 
THE  FOUR  MOONS  BY  GALILEO.— EFFECT  ON  THE  COPEENICAN  THEORY.— 
JUPITER'S  NOCTURNAL  HEAVENS. 

THE  SATELLITES  OF  JUPITER.— How  DISCOVERED.— THEIR  MAGNITUDE.— 
FORM  OF  THJ^R  ORBITS.— PERIOD  OF  REVOLUTION.— ECLIPSES.— TRANSITS.— 
OCCULTATIONS.— VELOCITY  OF  LIGHT  DISCOVERED.— TERRESTRIAL  LONGI- 
TUDE.— ROTATION  OF  THESE  MOONS  ON  AN  Axis. 


IN  passing  from  the  diminutive  asteroids  to  the  mag- 
nitude and  splendor  which  distinguish  the  vast  orb  which 
holds  the  next  position  in  the  planetary  system,  we  are 
the  more  disposed  to  adopt  the  theory  that  the  exceed- 
ing disparity  now  existing  in  the  magnitude  of  these 
neighboring  worlds  is  due  to  the  fact  that  the  asteroids 
are  but  a  few  of  the  fragments  of  some  object  in  which 
they  were  all  once  united.  We  shall  hereafter  present 
a  speculation  on  this  subject  which  seems  entitled  to 
consideration. 

The  planet  Jupiter  is  one  of  the  five  revolving  worlds 
discovered  in  the  primitive  ages.  Its  revolution  among 
the  fixed  stars  is  slow  and  majestic,  comporting  well  with 
its  vast  dimensions,  and  the  dignity  conferred  by  four 
tributary  worlds. 


JUPITER.  135 

Like  all  the  old  planets,  the  ancients  had  determined 
with  considerable  precision  the  period  of  revolution  of 
Jupiter,  and  his  relative  position  among  the  planetary 
worlds.  The  points  in  his  orbit  where  he  becomes  sta- 
tionary, the  arc  over  which  he  retrogrades,  and  his  period 
of  retrogradation,  were  all  pretty  well  determined  from 
the  early  observations. 

As  we  recede  to  greater  distances  from  the  sun,  the 
arc  of  retrogradation  diminishes  in  extent,  while  the  time 
employed  in  describing  these  arcs  must  by  necessity  in- 
crease. This  will  become  evident  if  we  recall  to  mind 
the  cause  of  this  apparent  retrogradation.  When  the 
sun,  earth,  and  planet,  are  all  on  the  same  straight  line, 
the  earth  and  planet  being  on  the  same  side  of  the  sun, 
then  the  planet  is  exactly  in  opposition.  The  earth  and 
planet  starting  from  this  line,  as  the  earth^  moves  the 
swifter  in  its  orbit,  at  the  end  of,  say,  twenty-four  hours, 
the  line  joining  the  earth  and  planet  will  take  a  direction 
such  that  it  will  meet  the  first  line  exterior  to  the  orbit 
of  the  planet,  as  seen  below : — 


0  E  P  is  the  line  on  which  the  three  bodies  are  found 
on  the  day  of  opposition.  At  the  end  of,  say,  twenty- 
four  hours,  the  earth  arrives  at  E'  in  its  orbit,  the  planet 
at  P',  and  then  the  planet  is  seen  from  the  earth  in  the 


136 


JUPITER. 


direction  E'  P'  S',  whereas  on  the  day  previous  it  was 
seen  in  the  direction  EPS.  Thus  it  appears  to  have 
moved  backwards  from  S  to  S'  among  the  fixed  stars, 
while  in  reality  it  has  moved  forward  in  its  orbit  from  P 
to  P'.  Admitting  the  orbits  to  be  circles  and  the  mo- 
tions to  be  uniform,  it  is  very  easy  to  locate  the  places  of 
the  earth  and  planet  on  successive  days  after  opposition, 
and  joining  those  places  by  straight  lines,  we  should  soon 
reach  a  position  in  which  the  lines  thus  drawn  on  con- 
secutive days  would  be  parallel.  There  the  planet  would 
appear  stationary  among  the  fixed  stars,  and  there  its 
advance  would  commence,  as  is  manifest  from  the  figure 
below : — 


in  which  S  is  the  sun,  E  E'  E"  E'"  the  successive  places 
of  the  earth,  P  P'  P"  P'"  the  successive  places  of  the 
planet.  The  lines  E  P  and  E'  P'  meet  on  the  side  op- 
posite the  sun,  the  lines  E'  P'  and  E"  P"  also  meet  on 
the  same  side,  but  E'"  P'"  and  E"  P"  are  parallels,  and 
in  P"  the  planet  becomes  stationary,  and  after  passing 
this  point,  the  earth  still  advancing,  the  lines  joining  the 
earth  and  planet  meet  on  the  side  next  the  earth,  and 
henceforward  the  motion  of  the  planet,  as  seen  from  the 


JUPITER. 


187 


earth,  must  continue  to  be  direct,  until  the  earth  coming 
round  again  to  occupy  the  conjunction  line,  previous  to 
which  the  stationary  point  will  be  passed,  and  the  retro- 
gradation  will  be  commenced. 

The  distance  of  any  planet  from  the  sun,  in  terms  of 
the  earth's  distance,  may  be  obtained  from  a  measure- 
ment of  the  arc  of  retrogradation  in  a  given  time,  say 
twenty-four  hours,  provided  we  know  the  periodic  time 
in  which  the  earth  and  planet  revolve  round  the  sun 
This  will  become  evident  from  the  figure  below —  • 


in  which  S  is  the  sun,  E  and  P  the  places  of  the  earth 
and  planet  on  the  day  of  opposition,  E'  and  P'  their 
places  at  the  end  of  twenty-four  hours.  E  E'  and  P  P' 
may  be  regarded  as  straight  lines,  as  they  are  very  short 
in  comparison  with  the  entire  circumference.  As  we  are 
supposed  to  know  the  periods  of  revolution  of  the  earth 
and  planet,  the  distances,  E'  E  and  P  P',  are  fractional 
parts  of  the  whole  circumference,  represented  by  one,  di- 
vided by  the  number  of  days  in  the  periodic  time.  The 
fraction  for  the  earth  is  ,  and  for  Jupiter  it  is 


In  the  right-angled  triangle,  E'  E  0,  we  know  the 


138  J  U  P  I  T  E  E  . 

value  of  E'  E,  and  the  angle,  E'  0  E,  equal  to  S'O  S", 
or  the  retrogradation  of  the  planet.  Hence  the  other 
parts  hecome  known  either  by  construction  or  the 
simplest  processes  of  trigonometry.  We  thus  determine 
the  value  of  E  0,  and  adding  S  E,  we  have  the  value 
of  S  0.  Then  in  the  triangle  S  P'  0,  we  have  the 
side  S  0,  just  determined,  also  the  angles  P'  S  0  and 
P'  0  S.  Hence  we  can  construct  the  triangle,  or  com- 
pute by  trigonometry  the  other  parts.  Thus  S  P',  the 
planet's  distance,  becomes  known. 

In  case  the  periodic  times  were  accurately  known,  and 
the  orbits  were  exact  circles,  this  mode  of  determining 
the  distance  of  a  superior  planet  would  be  sufficiently 
exact,  but  by  the  third  of  Kepler's  laws,  which  tells  us 
that  the  squares  of  the  periodic  times  are  proportional  to 
the  cubes  of  the  mean  distances,  we  perceive  that  the  en- 
tire problen?  of  the  planetary  distances  resolves  itself 
into  fixing,  with  all  possible  precision,  from  observation, 
the  periods  of  revolution,  and  then  in  obtaining  the  exact 
distance  of  any  one  of  them. 

We  have  already  stated  that  the  interval  elapsing  from 
the  passage  of  a  planet  from  one  side  of  the  ecliptic  to 
the  other,  up  to  the  same  again,  gives  the  period  of  rev- 
olution, in  case  we  correct  for  the  various  changes  which 
may  take  place  from  one  node-passage  to  the  next.  This, 
however,  in  the  case  of  a  planet  like  Jupiter,  whose 
orbital  plane  nearly  coincides  with  the  ecliptic,  becomes 
difficult  as  a  matter  of  observation,  and  hence  some  better 
method  must  be  employed.  This  is  best  accomplished 
by  observing  the  exact  time  of  opposition,  or  the  moment 
when  the  planet  is  180°  distant  from  the  sun. 

The  interval  between  two  such  oppositions  is  called 
a  synodical  revolution,  and  in  case  the  earth  did  not 


JUPITER.  189 

move,  would  be  the  planet's  period  of  revolution  around 
the  sun.  These  synodical  revolutions  would  be  all  pre- 
cisely equal  on  the  hypothesis  of  circular  orbits  and 
equable  motions.  But  as  the  planetary  orbits  are  ellip- 
tical, and  hence  the  motions  variable,  the  synodical  revo- 
lutions of  any  planet,  as  Jupiter,  will  vary  somewhat 
from  each  other  in  duration.  If,  however,  a  large  num- 
ber be  counted,  say,  as  many  as  have  occurred  in  a  thou- 
sand, or  even  two  thousand  years,  then  a  mean  period  is 
deduced  of  great  accuracy. 

This  is  possible,  as  we  have  the  oppositions  of  the  old 
planets,  recorded  by  the  ancients  with  sufficient  precision 
to  be  employed  in  such  a  discussion. 

To  derive  the  sidereal  revolution  from  the  synodical 
we  have  only  to  consider  that  the  two  bodies  set  out  from 
the  same  right  line.  The  earth's  velocity  is  known  ;  the 
time  required  for  the  earth  to  overtake  the  planet  is 
known  (the  synodical  revolution).  The  velocity  or  rate 
of  the  planet's  motion  is  required.  This  is  readily  found 
by  simple  proportion.  Take  the  following  example.  In 
a  mean  solar  day  the  earth  travels  in  its  orbit  (F.9856. 
A  mean  synodical  revolution  of  Jupiter  is  observed  to  be 
equal  to  398.867  solar  days.  But  the  earth  performs 
its  revolution,  and  comes  again  to  the  starting  point  in 
305.256  days,  and  then  must  travel  for  398.867— 
365.256=33.611  days  before  overtaking  Jupiter.  But 
in  33.611  days,  at  the  rate  of  0°.9856  per  diem,  the 
earth  will  travel  about  33°.928,  and  this  is  the  whole 
distance  made  by  Jupiter  in  398.867  days.  Hence,  his 
rate  per  diem  is,  ^^=4'  99=4'  59".2,  and  at  this 


rate  to  travel  360°  will  require  -~  =4.332d.   14L 

4  59  .2. 


140  JUPITER. 

2m.,  which  is  the  time  occupied  by  Jupiter  in  performing 
his  revolution  around  the  sun. 

These  methods  of  investigation,  which  are  perfectly 
simple,  were  employed  hy  the  ancients,  and  used  even  j?y 
Copernicus,  Kepler,  and  others,  and  furnished  the  ap- 
proximate values  of  the  periods  and  distances  employed 
in  the  researches  of  Kepler,  whereby  he  discovered  his 
celebrated  laws. 

PHYSICAL  CONSTITUTION  OF  JUPITER. — When  examined 
with  powerful  telescopes  the  surface  of  Jupiter  is  found  to 
be  diversified  with  shades  of  greater  or  less  depth,  forming 
parallel  bands  or  belts,  especially  about  the  equator  of  the 
planet. 

Upon  these  belts  well-defined  breaks,  irregularities, 
and  spots  are  discerned,  by  means  of  which  it  is  dis- 
covered that  the  face  of  Jupiter,  visible  at  any  given  time, 
is  completely  hidden  by  rotation  on  an  axis,  a  new  face 
appearing  at  the  end  of  a  little  less  than  Jive  hours. 
This  gives  a  period  of  axical  rotation  of  9h.  55m.  49.7s., 
as  the  result  of  investigations  similar  to  those  employed 
in  determining  the  period  of  rotation  of  Mars. 

When  the  apparent  diameter  of  Jupiter  is  accurately 
measured,  and  his  distance  is  taken  into  consideration, 
we  find  his  actual  diameter  to  be  nearly  90,000  miles, 
and  his  volume  to  be  equal  to  that  of  1,281  globes  such 
as  our  earth. 

The  dark  belts  which  encircle  the  equatorial  regions  of 
the  planet,  and  which  revolve  with  the  globe,  show  that 
the  axis  of  rotation  is  very  nearly  perpendicular  to  the 
plane  of  the  orbit. 

Thus  we  have  a  planet  twelve  hundred  and  eighty- 
one  times  la^er  than  our  earth,  rotating  on  an  axis,  but 
little  inclined  to  the  plane  of  its  orbit,  in  less  than  ten  hours 


JUPITER 


ALLA  VISTA.TENERIFFE  1856 


JUPITER.  141 

of  time,  and  sweeping  round  the  sun  in  about  twelve  of  our 
years,  at  a  mean  distance  of  about  485  millions  of  miles. 

The  streaks  and  dark  shades  which  distinguish  the 
equatorial  region  of  Jupiter  are  by  many  considered  to 
be  belts  of  clouds  floating  in  the  atmosphere  of  the 
planet,  thus  indicating  the  existence  of  all  the  great  ele- 
ments which  distinguish  the  earth.  In  consequence  of 
the  fact  that  the  axis  of  Jupiter  is  very  nearly  perpen- 
dicular to  the  plane  of  the  Orbit,  the  sun  will  always 
pour  his  rays  vertically  on  the  equator  of  the  planet, 
constituting  one  perpetual  summer  in  all  parts  of  the 
globe.  In  case  light  and  heat  are  governed  by  the  same 
laws  which  hold  on  the  earth,  the  inhabitants  of  Jupiter 
will  receive  from  the  sun  only  one  twenty-seventh  part 
as  much  light  and  heat  as  falls  on  the  earth.  What  mo- 
difications of  heat  may  be  effected  by  the  extensive  atmos- 
phere which  appears  to  surround  Jupiter  it  is  impos- 
sible to  conjecture.  "We  may  suppose,  without  reflection, 
that  a  world  would  be  only  dimly  illumined  whose  sun 
was  reduced  to  one  twenty-seventh  part  of  that  which 
lights  our  earth.  This,  however,  is  not  the  case,  as  any 
one  will  credit  who  has  ever  witnessed  the  flood  of  light 
poured  forth  from  the  smallest  portion  of  the  sun's  disk 
in  emerging  from  total  eclipse.  The  amount  of  light 
which  falls  on  Jupiter  far  exceeds  that  which  is  poured 
upon  the  earth  on  a  moderately  cloudy  day. 

When  we  measure  rigorously  with  tl  s  micrometer  the 
figure  of  Jupiter's  disk,  we  find  a  marked  deviation  from 
the  circular  outline.  This  is  analogous  to  the  figures  of 
the  earth  and  Mars,  and  indeed  the  same  peculiarity  (of 
which  a  satisfactory  account  will  be  given  hereafter)  dis- 
tinguishes all  the  planets.  In  Jupiter  the  equatorial  diam- 
eter exceeds  the  polar  by  more  than  six  thousand  miles. 


142  J  U  P  I  T  E  E . 

We  are  indebted  to  the  telescope  for  the  revelation  of 
the  highly  interesting  fact  that  Jupiter  is  attended  by  no 
less  than  four  moons  or  satellites,  nearly  all  of  them 
larger  than  our  own  moon.  These  satellites  were  dis- 
covered by  Galileo  in  1610,  soon  after  he  had  finished 
his  second  telescope,  which,  as  he  tells  us,  cost  him  in- 
credible pains,  and  which  bore  a  magnifying  power  of 
about  thirty  times.  The  discovery  of  these  moons  of 
Jupiter  may  be  regarded  as  among  the  most  important 
results  of  the  application  of  the  telescope,  if  we  take  into 
account  the  then  existing  condition  of  astronomical 
science.  The  scientific  world  was  just  in  a  transition 
state.  The  most  honest,  intelligent,  and  powerful  minds 
had  already  adopted  the  Copernican  theory,  but  in  the 
universities  and  other  schools  of  science,  as  well  as  in  the 
church,  the  system  of  Ptolemy  still  reckoned  among  its 
supporters  a  host  of  learned  and  dignified  men.  The 
beautiful  miniature  of  the  solar  system  presented  in 
Jupiter  and  his  moons,  as  given  by  Copernicus,  could 
not  fail  to  exert  a  most  powerful  influence  over  all  candid 
anil  unprejudiced  minds.  Here  was  presented  to  the  eye 
a  central  orb  and  about  it  a  scheme  of  dependent  worlds 
revolving  in  circular  orbits,  and  with  such  elegant  sim- 
plicity as  to  shame  the  cumbrous  complexity  which  dis- 
tinguished the  epicyclical  theory  of  the  old  Greek  school. 
It  is  not  at  all  surprising  that  Galileo,  the  discoverer  of 
this  beautiful  system,  should  have  become  one  of  the 
most  ardent  supporters  of  the  doctrines  of  Copernicus. 

These  satellites  of  Jupiter  revolve  in  orbits  whoso 
planes  are  nearly  coincident  with  the  equator  of  their 
primary.  The  exterior,  or  most  distant  of  the  four, 
revolves  in  an  orbit  somewhat  inclined  to  the  plane  of 
Jupiter's  equator,  but  the  three  inner  satellites,  at  every 


JUPITER.  143 

revolution,  eclipse  the  sun  to  the  inhabitants  of  Jupiter, 
and  are  themselves  eclipsed  in  passing  through  the  shadow 
of  their  primary.  The  same  phases  which  mark  the 
revolution  of  our  moon  are  also  exhibited  by  Jupiter's 
moons,  and  the  periods  of  revolution  of  three  of  the  satel- 
lites are  so  adjusted  that  one  of  them  must  be  full  when 
the  other  two  are  new. 

The  nocturnal  heavens,  as  seen  from  this  grand  orb, 
must  be  inexpressibly  magnificent.  Besides  the  same 
glittering  constellations  which  are  seen  from  earth,  the 
sky  of  Jupiter  may  be  adorned  with  no  less  than  four 
moons,  with  their  diverse  phases,  some  waxing  or  waning, 
some  just  rising  or  setting,  some  possibly  just  entering 
into  or  emerging  from  eclipse. 

The  whole  of  this  splendid  celestial  exhibition,  sweep- 
ing across  the  heavens,  rising,  culminating,  and  setting, 
in  less  than  five  hours  of  our  time.  Such  are  the  scenes 
witnessed  by  the  inhabitants  of  Jupiter,  if  such  there  be. 

THE  SATELLITES  OP  JUPITER. — As  already  stated, 
these  tributary  worlds  were  discovered  by  Galileo  in 
1610.  On  the  evening  of  January  the  8th,  of  that  year, 
having  completed  his  second  telescope,  capable  of  bearing 
a  magnifying  power  of  thirty  times,  he  went  to  his  garden 
to  test  its  quality  by  an  examination  of  Jupiter.  Near 
the  planet  he  noticed  three  small  stars,  nearly  in  a  straight 
line,  passing  through  the  center  of  Jupiter.  He  sup- 
posed them  to  be  fixed  stars,  but  carefully  noted  their 
positions  with  reference  to  Jupiter  and  to  each  other. 
On  the  following  night,  he  remarked  that  there  was  a 
manifest  change  in  the  relative  places  of  these  stars  and 
the  planet  which  could  hardly  be  accounted  for  by  the 
motion  of  Jupiter  in  his  orbit. 

Galileo  began  to  suspect  the  true  nature  of  the  stars 


144  J  U  P  I  T  E  E . 

which  had  attracted  his  attention,  and  seeing  clearly  the 
immense  importance  of  such  a  discovery,  awaited  with 
great  impatience  the  coming  of  the  next  evening  to  con- 
firm Lis  conjectures.  Clouds,  however,  coming  up  dis- 
appointed his  hopes,  and  it  was  not  until  the  evening  of 
the  14th  that  he  was  again  permitted  to  direct  his  tele- 
scope to  the  planet,  when  he  found,  to  his  great  delight, 
not  only  the  three  stars,  still  in  close  proximity  to  the 
planet,  but  he  also  detected  a  fourth  one,  whose  appear- 
ance and  position  were  such  that  he  announced  at  once 
the  discovery  of  four  moons  resembling  our  own,  and  re- 
volving about  the  planet  Jupiter  as  their  central  orb. 

This  announcement  created  the  greatest  excitement  in 
the  astronomical  world.  Its  effect  on  the  old  theory  of 
astronomy  was  at  once  perceived,  and  the  disciples  of 
Ptolemy  determined  that  they  would  never  believe  in  the 
existence  of  any  such  pestilent  worlds.  Some  of  them 
actually  refused  to  do  so  much  as  look  through  the  tube 
of  Galileo,  declaring  the  whole  was  a  deception,  and  un- 
worthy the  attention  of  a  true  philosopher. 

The  discovery  was  not  the  less  real  because  its  truth 
was  denied,  and  to  this  important  addition  to  the  bodies 
which  constitute  our  system  modern  science  is  indebted 
for  some  of  its  most  elegant  discoveries. 

The  great  distance  at  which  we  are  compelled  to  exam- 
ine these  bodies  has  rendered  it  difficult  to  obtain,  even 
with  our  most  delicate  instruments,  satisfactory  measures 
of  the  diameters  of  these  satellites.  Approximate  meas- 
ures have  been  obtained  from  which  we  learn  that  the 
nearest  satellite  has  a  diameter  of  about  2,500  miles,  the 
second,  2,068;  the  third,  2,377;  the  fourth,  2,800 
miles.  We  name  them  in  the  order  of  their  distances 
from  the  primary. 


JUPITER.  145 

By  careful  measures  of  the  elongations,  or  greatest 
distances  to  which  these  bodies  recede  from  their  primary, 
the  magnitude  and  form  of  their  orbits  have  been  well 
determined.  The  first  satellite  is  thus  found  to  revolve 
round  Jupiter  in  an  orbit  nearly  circular,  whose  diameter 
is  260,000  miles,  in  a  period  of  Id.  18h.  28m.  The 
plane  on  which  the  orbit  lies  is  inclined  to  the  plane  of 
Jupiter's  orbit,  under  an  angle  of  3°  05'  30",  or  less,  by 
nearly  one-half,  than  the  angle  made  by  the  moon's  orbit 
with  that  of  the  earth.  The  smallness  of  this  angle, 
the  nearness  of  the  satellite  to  its  primary,  the  immense 
magnitude  of  the  primary  and  the  distance  from  the  sun, 
combine  to  produce  an  eclipse  of  the  first  satellite  at 
every  revolution,  while,  in  like  manner,  an  eclipse  of 
the  sun  takes  place  quite  as  frequently,  from  the  fact  that 
the  shadow  of  the  satellite  falls  on  the  planet  at  every 
conjunction  of  the  satellite  with  the  sun.  These  state- 
ments are  not  mere  conjectures.  They  are  verified  by 
the  telescope,  for  these  eclipses  of  the  satellite  and  the 
shadows  cast  on  the  primary  are  distinctly  seen  from  the 
earth,  and  furnish  the  data  whereby  the  periods  of  revo- 
lution are  determined  with  great  precision.  When  Jupi- 
ter is  in  opposition  it  often  occurs  that  the  satellite  when 
on  the  hither  side  of  the  primary,  is  seen  projected  on  the 
disk  of  the  planet  as  a  round  bright  spot,  while  the 
shadow  of  the  same  body  may  be  seen  in  close  proximity 
as  a  round  black  spot.  Any  eye,  situated  within  the 
limits  of  this  shadow,  will  witness  an  eclipse  of  the  sun 
precisely  such  as  is  produced  on  earth  by  the  shadow  of 
the  moon.  The  passage  of  the  satellite  across  the  disk 
of  Jupiter  is  called  a  transit.  From  this  position  the 
moon  of  Jupiter  revolves  round  half  its  orbit,  and  then  by 
necessity  passes  across  the  cone  of  shadow  cast  by  the 

7 


146 


JUPITER. 


primary  in  a  direction  opposite  the  sun.  Here  we  be- 
hold an  eclipse  of  the  secondary,  as  its  light  is  extin- 
guished on  entering  the  shadow,  and'  is  only  regained 
after  passing  beyond  the  limits  of  the  shadow,  thus  de- 
monstrating beyond  a  doubt  the  fact  that,  like  our  moon, 
these  secondaries  of  Jupiter  shine  only  by  reflecting  the 
light  of  the  sun. 

In  case  Jupiter  were  at  rest,  it  is  evident  that  the  ob- 
servations of  these  eclipses  would  give  the  exact  period 
of  revolution  of  the  satellite,  which  would  be  precisely 
the  interval  from  one  eclipse  to  the  next.  The  fact  that 
the  earth  is  in  motion  would  not  affect  the  time  of  recur- 
rence of  the  eclipse,  for  this  would  be  entirely  independ- 
ent of  the  place  of  the  spectator,  provided  he  sees  the 
disappearance  of  the  satellite  at  the  moment  its  light  is 
extinguished.  It  is  manifest  that  the  motion  of  Jupiter 
in  his  orbit  will  change  the  position  of  the  axis  of  the 
shadow,  and  as  the  satellite  revolves  in  the  same  direc- 
tion in  which  the  shadow  advances,  it  is  clear  that  the 
time  from  one  eclipse  to  the  next  is  longer  than  the  true 
period  of  revolution  of  the  satellite,  by  a  quantity  easily 
computed  from  the  known  orbital  velocity  of  the  planet, 
as  may  be  seen  from  the  figure  below,  where-r- 


JUPITER.  147 

S  is  the  sun's  place,  E,  the  earth,  J,  Jupiter  in  opposi- 
tion, M,  the  satellite  in  eclipse.  At  the  end  of  one 
exact  revolution  of  the  satellite,  Jupiter  has  reached  J', 
the  satellite  is  at  M',  but  the  axis  of  shadow  is  now  J'  M". 
and  the  center  of  the  eclipse  will  not  occur  until  the 
satellite  reaches  M",  passing  over  the  angle  M"  J'  M'. 
This  angle  is  precisely  equal  to  the  angular  motion  from 
eclipse  to  eclipse,  a  quantity  easily  determined.  The 
satellite  will  then  revolve  360°,  +  the  angle  J  S  J',  or 
M'  J'  M",  in  the  interval  from  one  eclipse  to  the  next, 
hence  the  rate  per  hour  becomes  known,  and  gives  at  once 
the  period  of  revolution. 

Galileo  devoted  himself  for  many  years  to  a  careful 
observation  of  the  eclipses  of  Jupiter's  moons,  and  finally 
constructed  tables  whereby  these  eclipses  might  be  pre- 
dicted with  tolerable  precision.  His  successors  devoted 
much  time  to  the  same  subject,  for  a  reason  we  will  give 
hereafter.  Long  study  of  these  phenomena  revealed  the 
curious  fact  that  the  interval  from  one  eclipse  to  the  next 
did  not  fulfil  the  prediction  based  on  the  foregoing  reason- 
ing. The  place  of  the  earth  seemed  in  some  mysterious 
way  connected  with  the  time  at  which  the  eclipse  occur- 
red. This  may  to  some  appear  very  reasonable,  but,  in 
fact,  on  the  hypothesis  that  at  the  moment  of  the  extinc- 
tion of  a  luminous  object  it  ceases  to  be  visible,  the  place 
of  the  earth  in  its  orbit  or  the  position  of  the  observer 
could  in  no  way  affect  the  moment  of  the  satellite's  dis- 
appearance by  entering  the  shadow  of  its  primary.  This 
will  become  manifest  from  a  very  simple  illustration. 
Suppose  the  persons  in  a  large  circular  hall  to  be  gazing 
on  the  light  of  a  taper,  and  the  taper  is  suddenly  extin- 
guished by  being  blown  out,  every  observer  will  certainly 
lose  the  light  at  the  same  absolute  moment,  admitting 


148  JUPITER. 

the  fact  that  the  light  dies  at  the  instant  of  extinction  to 
every  eye.  Let  us  apply  this  illustration  to  the  eclipses 
of  Jupiter's  moons.  They  are  only  seen  when  the  sun- 
light falls  on  them.  Cut  off  from  them  the  sunlight  by 
entering  the  shadow  of  the  primary,  and  admitting  this 
entrance  to  be  instantaneous,  every  eye  everywhere  should 
lose  the  light  at  the  same  moment  of  absolute  time. 

The  earth's  position  in  its  orbit  ought,  therefore,  to 
have  no  effect  on  the  time  of  the  eclipse,  and  yet  it  be- 
came clearly  manifest  that  the  earth's  place  was  in  some 
way  connected  with  certain  irregularities  in  the  intervals 
of  these  remote  eclipses.  This  matter  will  be  best  illus- 
trated from  the  figure  below,  in  which  S  represents 


J       s 


the  sun,  E  E'  E"  E'"  the  earth's  orbit,  J  Jupiter, 
and  S  the  satellite.  It  was  found  that  when  the 
earth  was  at  E,  or  nearest  to  Jupiter,  the  interval  from 
eclipse  to  eclipse  grew  longer  as  the  earth  receded  from 
Jupiter.  At  E'  the  interval  was  at  a  maximum.  It 
now  diminished  by  slow  degrees,  becoming  nearly  station- 
ary at  E",  then  growing  shorter,  reached  a  minimum  at 
E"',  after  which  a  slow  increase  ^ras  noticed  up  to  E, 
and  so  on  in  every  revolution  of  the  earth  in  its  orbit. 
Due  account,  of  course,  must  be  taken  of  the  orbital 


JUPITER.  149 

movement  of  Jupiter.  In  case  the  student  is  ignorant  of 
the  explanation  of  these  variations  in  the  synodical  revo- 
lutions of  the  moons  of  Jupiter,  he  may  test  his  own 
powers  of  discovery  hy  a  close  examination  of  the  facts  • 
as  above  presented.  All  the  satellites  gave  evidence  of 
the  same  facts,  and  the  irregularities  were  found  to  follow 
in  the  same  order,  reaching  their  maxima,  minima,  and 
stationary  points  at  the  same  time,  or  when  the  earth 
was  at  the  same  point  of  its  orhit. 

More  than  fifty  years  passed  away  without  any  satis- 
factory explanation  of  the  facts  and  phenomena  above  re- 
corded, when,  in  1675,  Roemer  was  at  length  successful 
in  solving  the  mystery,  and  found  it  due  to  the  progress- 
ive motion  of  light,  which  up  to  this  time  had  been  con- 
sidered by  all  philosophers  as  instantaneous  in  its  effects ; 
that  is,  if  a  luminous  body  were  created,  all  eyes,  no 
matter  how  remotely  placed,  would  see  the  light  at  the 
same  moment  of  time.  As  the  velocity  of  light,  deduced 
from  these  investigations,  is  so  enormous,  no  less  than 
192,000  miles  in  one  second,  we  will  enter  into  the 
explanation  somewhat  minutely.  Suppose  a  luminous 
body,  as  in  the  figure  below,  at  S,  suddenly  to  be  ex- 
tinguished, the  stream  of  light  flowing  from  the  body  is 

#  A  B 

S 

at  once  cut  of,  and  when  the  last  particles  or  wave  passes 
a  spectator  at  A,  at  that  moment  he  will  mark  the  ex- 
tinction of  the  light,  while  to  the  spectator  at  B  the 
really  extinct  luminous  body  will  remain  visible  until  the 
last  particles  of  the  stream  of  its  light  pass  B,  and  then 
the  body  vanishes  to  the  spectator  at  B.  Suppose  the 
body  to  thus  disappear  periodically,  A  and  B  will,  while 


150  JUPITER. 

^ 

they  remain  stationary,  note  the  intervals  from  one  dis- 
appearance to  the  next  to  be  precisely  equal,  and  the  in- 
terval, as  observed  by  A,  though  beginning  at  an  earlier 
absolute  moment  of  time,  will  be  equal  to  the  interval, 
as  observed  at  B.  Let  us  now  suppose,  that  after  a  dis- 
appearance, and  before  the  next,  A  removes  to  B,  it  is 
manifest  that  the  duration  or  period  whose  beginning  was 
observed  at  A,  but  whose  ending  was  noted  at  B,  will  be 
longer  than  it  was  before  by  an  amount  of  time  required 
for  the  stream  of  light  to  pass  from  A  to  B.  The  reverse 
would  be  true  if  B  changed  his  position  to  A. 

These  principles  are  precisely  applicable  to  the  case 
under  consideration.  If  the  earth's  orbit  were  a  straight 
line,  with  a  length  equal  to  A  B,  the  conditions  would  be 
identical.  The  nearly  circular  figure  of  the  earth's  orbit 
produces  the  variations  already  noticed.  When  the  earth 
is  rapidly  receding  from  the  source  of  light,  the  dura- 
tion of  the  synodical  revolution  of  Jupiter's  moon  will  be 
increased  by  the  time  required  for  the  light  to  pass  over 
the  space  traversed  by  the  earth  during  the  synodic  rev- 
olution. This  period  amounts  to  some  seventeen  days 
for  the  fourth  satellite.  But  the  earth  travels  some 
68,000  miles  an  hour,  or  in  seventeen  days  nearly  thirty 
millions  of  miles,  so  that  the  synodical  revolution,  when 
longest,  will  exceed  the  same  period  when  shortest  by  an 
amount  equal  to  the  double  time  required  by  light  to 
travel  30,000,000  of  miles.  This  difference  between  the 
maximum  and  minimum  synodic  periods,  proved  to  be 
about  five  minutes,  and  hence  it  became  evident  that 
light  must  fly  at  the  rate  of  sixty  millions  of  miles  in  five 
minutes  or  12,000,000  miles  in  one  minute  or  192,000 
miles  per  second. 

Should  this  result  appear   incredible  we   shall  find 


JUPITER.  151 

hereafter  abundant  confirmation  of  its  truth  by  a  train 
of  reasoning  and  phenomena  entirely  distinct  from  what 
have  just  been  given. 

In  case  light  travels  with  a  finite  velocity  we  cannot 
fail  to  perceive  that  this  fact  will  introduce  important 
modifications  in  all  observations  designed  to  fix  the  places 
of  the  heavenly  bodies  at  a  given  moment  of  time.  Since 
the  earth  is  sweeping  through  space  with  great  velocity 
even  this  fact  will  produce  a  certain  displacement  in  the 
apparent  place  of  a  fixed  luminous  body.  When  the 
body  under  observation  is  in  motion,  the  velocity  of  light 
being  finite,  it  is  clear  that  the  light  which  fells  on  the 
eye  of  the  spectator,  and  which  enables  him  to  see  the 
object,  is  not  the  light  emitted  at  the  moment  the  object 
is  seen.  Thus,  the  planet  Jupiter  is  distant  from  the 
earth,  say,  480  millions  of  miles.  To  travel  this  distance 
his  light  must  occupy  no  less  than  forty  minutes,  during 
which  time  Jupiter  has  advanced  in  his  orbit  about  one- 
third  of  his  own  diameter.  During  the  same  time  the 
earth  has  traveled  in  its  orbit  a  certain  distance  nearer  to 
or  further  from  Jupiter,  which  must  be  taken  into  account 
in  our  effort  to  fix  the  absolute  position  of  the  planet's 
center  at  a  given  moment.  This  subject  will  be  resumed 
when  we  come  to  consider  the  means  and  instruments  em- 
ployed in  astronomical  observation. 

The  satellites  of  Jupiter  have  furnished,  in  their  eclipses, 
the  earliest  method  of  resolving  the  great  problem  of 

TERRESTRIAL  LONGITUDE. — The  position  of  any  place 
on  the  earth's  surface  is  determined  by  fixing  its  distance 
from  the  equator  of  the  earth,  north  or  south,  called  the 
latitude,  and  also  its  distance  east  or  west  of  any  given 
meridian  line,  called  the  longitude.  The  first  of  these 
elements  is  very  readily  determined.  In  case  a  place  is 


152  JUPITER. 

situated  on  the  equator,  its  latitude*  is  zero,  and  to  any 
spectator  at  this  place,  as  we  have  already  shown,  the 
poles  of  the  earth  and  heavens  will  lie  on  the  horizon. 
Leaving  the  equator  and  traveling  due  north  along  a 
meridian  line,  for  every  degree  we  go  north,  it  is  evident 
the  pole  of  the  heavens  will  rise  one  degree  above  the 
horizon;  and  when  we  reach  the  north  pole  of  the  earth, 
the  north  pole  of  the  heavens  will  be  on  the  zenith,  or 
ninety  degrees  above  the  horizon. 

Thus  it  appears  that  the  latitude  of  any  place  is  equal 
to  the  elevation  of  the  pole  above  the  horizon  of  the 
place,  and  to  fix  the  latitude  we  have  only  to  measure  this 
angle  of  elevation  with  a  suitable  instrument,  and  apply 
certain  corrections,  to  be  hereafter  explained.  The  pro- 
blem of  the  longitude  does  not  admit  of  so  easy  a  solu- 
tion. To  determine  accurately  longitude  at  sea  is  a  mat- 
ter of  the  highest  importance  to  commerce  and  navigation, 
a  problem  for  whose  solution  maritime  nations  have  in 
modern  times  offered  large  rewards.  The  safety  of  a 
vessel,  its  crew  and  cargo,  depends  on  learning  by  some 
method  its  exact  position  on  the  surface  of  the  ocean, 
where  there  are  no  permanent  objects  on  our  globe  to 
mark  its  place  ;  and  it  is  only  from  the  celestial  sphere 
that  it  becomes  possible  to  select  fixed  objects  which  may 
reveal  to  the  mariner  the  dangers  by  which  he  is  sur- 
rounded. 

The  latitude,  as  we  have  seen,  is  readily  obtaioed; 
not  so  the  longitude,  which  had,  up  to  time  of  Galileo, 
been  regarded  as  almost  an  impossible  problem  at  sea. 
The  great  Florentine  astronomer  saw  in  the  eclipses  of 
the  moons  of  Jupiter  the  means  of  solving  this  highly 
important  problem,  and  to  this  end  he  devoted  many 
years  to  most  diligent  and  careful  observation  of  these 


JUPITEK.  %     153 

eclipses,  with  a  view  to  be  able  to  predict  their  coming, 
months  or  even  years  in  advance.  We  will  now  explain 
how  these  predicted  eclipses  of  Jupiter's  satellites,  con- 
joined with  their  actual  observation,  may  be  employed 
in  the  determination  of  terrestrial  longitude. 

As  the  earth  rotates  on  its  axis  with  uniform  velocity, 
the  360  degrees  of  the  earth's  equator  are  fairly  repre- 
sented by  twenty-four  hours  of  time.  Thus  an  hour  of 
time  is  equal  to  15°  of  longitude,  a  minute  of  time  is 
equal  to  4'  of  longitude,  a  second  of  time  is  equal  to  4" 
of  longitude.  The  difference  of  longitude,  then,  of  any 
two  places  on  the  earth's  surface  is  nothing  more  than 
the  difference  of  local  time,  for  a  mean  time  solar  clock 
marks  Oh.  00m.  OOs.  when  the  center  of  an  imaginary 
sun,  moving  with  the  mean  or  average  velocity  of  the 
true  sun,  reaches  the  meridian  of  the  place  in  question. 
A  place  west  of  the  first  one  will  have  the  center  of  the 
mean  sun  on  its  meridian  later  by  an  amount  of  time 
equal  to  the  exact  difference  of  longitude.  It  is  clear, 
then,  that  if  any  phenomenon,  such  as  the  sudden  extinc- 
tion of  a  fixed  star,  could  be  noted  by  two  observers  in 
different  places,  each  will  record  the  moment  of  disap- 
pearance in  his  own  local  time,  and  an  inter-comparison 
of  these  records  will  give  at  once  the  difference  of  longi- 
tude between  the  two  stations. 

Suppose  it  were  possible  to  predict  that  the  bright 
star  Vega,  in  the  constellation  of  the  Lyre,  would  sud- 
denly disappear  on  the  first  day  of  January,  1870,  at 
Oh.  00m.  OOs.  mean  time  at  Greenwich,  England,  this 
fact  being  known  and  published,  vessels  at  sea  on  long 
voyages,  in  all  parts  of  the  globe,  having  the  star  above 
their  horizon,  by  watching  for  this  phenomenon,  and  by 
noting  the  moment  of  disappearance  in  their  local  time, 


154      *  JUPITEK. 

would  determine  their  longitude  from  Greenwich.  All 
observers  recording  the  disappearance  before  the  pre- 
dicted time  would  be  in  east  longitude,  while  those  re- 
cording the  same  phenomenon  later  than  the  predicted 
time  would  be  in  west  longitude,  and  as  many  hours, 
minutes  and  seconds  west  as  was  indicated  by  their  local 
time. 

Now,  at  sea,  very  simple  methods,  as  we  shall  show 
hereafter,  may  be  employed  to  obtain  the  local  time,  and 
thus,  were  it  possible  to  predict  a  multitude  of  such  phen- 
omena as  above  recorded  occurring  every  day  or  two, 
for  years  in  advance,  seamen  on  long  voyages,  providing 
themselves  with  these  predictions,  would  have  the  means 
of  fixing  their  longitude  as  often  as  any  one  of  those  pre- 
licted  phenomena  could  be  observed. 

The  eclipses  of  the  moons  of  Jupiter  are  precisely  like 
the  phenomenon  of  the  sudden  extinction  of  a  star.  As 
these  moons  shine  only  by  reflected  light,  the  moment 
they  enter  the  shadow  of  their  primary  they  vanish  from 
the  sight,  or  are,  to  all  intents  and  purposes,  extin- 
guished ;  and  as  these  eclipses  are  constantly  recurring 
at  very  short  intervals,  Galileo  saw  at  once  the  use  to 
which  they  might  be  devoted  in  the  resolution  of  this 
great  problem  of  terrestrial  longitude. 

Before  they  could  be  thus  used  it  became  necessary 
to  master  completely  their  laws,  so  that  the  moment  of 
eclipse  might  be  accurately  predicted  years  in  advance. 
Though  the  Tuscan  philosopher  did  not  live  long  enough 
to  perfect  and  apply  his  great  discovery,  his  successors  in 
modern  times  have  fully  carried  out  and  applied  what 
was  so  admirably  conceived  and  so  carefully  com- 
menced. 

An  attentive  examination  of  the  luminosity  of  Jupi- 


JUPITER.  155 

ter's  moons  reveals  the  curious  fact  that  it  is  variable, 
increasing  and  decreasing  at  regular  intervals,  equal  to 
the  periods  of  revolution  in  their  orhits,  whence  it  has 
been  inferred  by  Sir  William  Herschel  and  others  that 
each  of  these  satellites  rotates  (like  our  moon)  upon  an 
axis  in  the  exact  time  in  which  it  revolves  about  the 
primary. 


CHAPTER    VIII. 

SATURN,  THE  SEVENTH  PLANET  IN  THE  ORDER  Of  DIS- 
TANCE FROM  THE  SUN,  SURROUNDED  BY  CONCENTRIC 
RINGS,  AND  ATTENDED  BY  EIGHT  SATELLITES. 


THB  MOST  DISTANT  OF  THE  OLD  PLANETS.— ITS  LIGHT  FAINT,  BUT  STEADY.— 
SYNODIOAL  EEVQLUTION.— THE  SIDEREAL  BEVOLUTION.— ADVANCES  IN  TELE- 
SCOPIC DISCOVEBT.— GALILEO  ANNOUNCES  SATURN  TO  BE  TRIPLE.— HUYGENS 
DISCOVERS  THE  KING.— DIVISION  OF  THE  KING  INTO  Two.— CASSINI  AN- 
NOUNCES THE  OUTER  EING  THE  BRIGHTER. — MULTIPLE  DIVISION. — SHADOW 
OF  THE  PLANET  ON  THE  EING. — BELTS  AND  SPOTS. — PERIOD  OF  EOTATIOX 
OF  THE  PLANET  AND  EING.— DISAPPEARANCE  OF  THE  EING  EXPLAINED.— THB 
,  DUSKY  EING. 

SATELLITES  OF  SATUEN.— BY  WHOM  DISCOVERED.— EIGHT  IN  NUMBER.— 
THEIR  DISTANCES  AND  PERIODS. — SATURN'S  ORBIT  THE  BOUNDARY  OF  THB 
PLANETARY  SYSTEM,  AS  KNOWN  TO  THE  ANCIENTS. 


WE  now  reach,  in  our  outward  journey  from  the  sun, 
the  most  distant  world  known  to  the  ancients,  revolving 
in  an  orbit  of  vast  magnitude,  and  in  a  period  nearly 
thirty  times  greater  than  that  of  our  earth.  Saturn,  on 
account  of  his  immense  distance,  shines  with  a  fainter 
light  than  either  of  the  old  planets,  though  still  a  con- 
spicuous object  among  the  fixed  stars.  Its  light  is  re- 
markably steady,  without  the  scintillations  which  dis- 
tinguish the  stars,  and  the  brilliant  glare  which  is  shown 
by  Venus  and  Jupiter.  There  is  a  yellowish  or  golden 
hue  to  this  planet  which  is  not  lost  when  seen  through 
the  most  powerful  telescopes. 

Such  is  the  planet  Saturn  as  known  to  the  old  astrono- 
mers, and  as  seen  by  the  unaided  vision.  Its  movement 


SATURN:  157 

among  the  fixed  stars  is  distinguished  by  the  same  phen 
omena  which  we  have  found  to  exist  among  all  the  plan 
ets.     Being  the  most  remote  of  all  the  old  satellites  of 
the  sun,  its  stations  are  the  best  defined,  its  arc  of  retro- 
gradation  the  shortest,  and  the  period  employed  in  this 
retrograde   movement  is   longest.      From   observations 
made  during  opposition,  and  by  trains  of  reasoning  iden- 
tical with  those  laid  down  in  our  examination  of  Jupi- 
ter, the  periodic  time  and  mean  distance  of  Saturn  are 
concluded. 

Owing  to  the  very  slow  motion  of  this  planet  in  its 
orbit,  the  earth  will  pass  between  it  and  the  sun,  or  bring 
it  into  opposition,  in  a  little  over  378  days ;  that  is,  Saturn 
and  the  earth  starting  from  the  same  straight  line,  pass- 
ing through  the  sun,  the  earth  makes  its  revolution, 
comes  up  to  the  starting  point,  and  then  overtakes 
Saturn  in  about  twelve  days  and  three-quarters.  The 
earth's  period  must  then  be  to  that  of  Saturn  as  twelve 
days  and  three-quarters  is  to  378,  or  as  one  to  thirty, 
roughly. 

This  determination  is  a  matter  of  such  simplicity  that 
any  one,  almost  without  instruments,  may  make  the  ob- 
servations which  give  the  data  for  the  computation.  The 
opposition  is  observed  when  Saturn  is  180°  from  the  sun, 
and  we  have  only  to  count  the  days  from  one  opposition 
to  the  next  to  obtain  the  synodical  revolution. 

Such  were  the  few  facts  known  to  astronomy  touching 
this  distant  orb  prior  to  the  discovery  of  the  telescope. 
The  immense  multiplication  and  extension  of  human 
vision  effected  by  the  invention  and  improvement  of  that 
instrument  is  in  no  case  more  signally  displayed  than  in 
the  successive  revelations  which  have  been  made  in  the 
physical  constitution  of  Saturn,  and  the  extraordinary 


158  SATURN. 

appendages  and  scheme  of  dependent  worlds  now  known 
to  revolve  around  him. 

In  1610,  the  year  in  which  Galileo  first  applied  the 
telescope  to  an  examination  of  the  celestial  orbs — the 
year  in  which  he  announced  the  discovery  of  Jupiter's 
moons — an  examination  of  Saturn  resulted  in  the  strange 
and  anomalous  discovery  that  his  disk  was  not  circular, 
like  all  the  other  planets,  but  elongated,  as  though  two 
smaller  planets  overlaid  a  larger  central  one  extending 
somewhat  to  the  right  and  left  of  the  center.  This  re- 
markable figure  Galileo  announced  to  his  astronomical 
contemporaries  under  the  form  of  a  puzzle  produced  by 
a  transposition  of  the  Latin  sentence — 

"  Altissimum  plane  tarn  tergenimum  observavi." 

UI  have  observed  the  most  distant  of  all  the  planets 
to  be  triple." 

This  mode  of  presenting  the  discovery  was  adopted  by 
the  Florentine  astronomer  to  establish  his  priority,  as 
many  of  his  great  discoveries  were  claimed  by  some  of 
his  opponents,  while  the  truth  of  all  was  most  obstinately 
disputed  by  others.  It  was  urged,  even  in  the  case  of 
Jupiter's  moons,  that  these  were  mere  illusions,  the  off- 
spring of  the  heated  imagination  of  the  ambitious  philoso- 
pher, and  that  other  eyes  could  never  verify  these  pre- 
tended discoveries.  We  can  readily  imagine  what  must 
have  been  the  feelings  of  Galileo  when,  not  many  months 
after  the  discovery  of  the  triple  character  of  Saturn,  he 
was  compelled  to  acknowledge  that,  even  as  seen  through 
his  most  powerful  telescope,  the  planet  was  exactly  cir- 
cular, with  an  outline  as  sharp  and  perfect  as  that  of 
Jupiter.  He  exclaims,  "Can  it  be  possible  some  demon 
has  mocked  me !"  He  did  not  live  to  explain  this  re- 


SATURN.  159 

markable  change,  but  he  saw  the  triple  form  restored, 
and  discovered  these  periodical  transmutations  of  figure, 

Fifty  years  later,  in  1659,  Huygens,  with  more  power- 
ful telescopes,  discovered  the  true  figure  of  Saturn,  and 
found  the  triple  form  seen  by  Galileo  to  be  produced 
by  the  fact  that  the  round  planet  was  encircled  by  a 
broad,  flat  ring  of  immense  diameter,  and  so  situated 
that  the  spectator  on  the  earth  can  never  see  it  in  a 
direction  perpendicular  to  its  plane.  Hence,  although 
circular  in  form,  the  direction  of  the  visual  ray  gives  it 
an  oval  or  elliptical  figure.  Huygens  distinctly  per 
ceived  the  dark  space  intervening  between  the  body  of  the 
planet  and  the  ring,  right  and  left,  which  had  escaped 
the  eye  of  Galileo  with  a  less  perfect  telescope.  Hence, 
the  Florentine  astronomer  only  saw  the  planet  elongated, 
and  pronounced  it  triple.  Huygens  explained  the  mys- 
terious change  of  figure  which  had  so  perplexed  Galileo, 
and  found  it  due  to  the  fact  that  the  ring  is  extremely 
thin,  so  thin,  indeed,  that  when  the  earth  chances  to  hold 
a  place  such  that  the  plane  of  the  ring  produced  passes 
through  the  earth  and  the  ring  comes  to  be  presented  to 
the  spectator  edgewise,  not  even  the  telescope  of  Huygens 
could  discern  the  fibre  of  light  presented  by  the  rim,  or 
circumference  of  the  ring,  when  thus  located,  and  to  them 
the  disappearance  was  complete,  leaving  the  planet  round, 
clear,  and  well-defined. 

In  1665,  what  had  hitherto  been  regarded  as  one 
broad,  flat  ring,  was  observed  to  be  divided  into  two  por- 
tions by  a  dark  line,  which,  wider  favorable  circum- 
stances, was  traced  entirely  round  the  ring.  This  dis- 
covery was  confirmed  by  the  elder  Cassini,  in  1675,  who 
also  discovered  the  unequal  brilliancy  of  the  two  rings, 
the  outer  one  being  the  brighter.  He  also  was  the  first 


160  SATURN. 

to  announce  the  existence  of  a  dark  stripe  or  belt  sur- 
rounding the  equator  of  the  planet.  Other  discoveries, 
such  as  additional  belts,  the  shadow  of  the  planet  on  the 
ring,  the  shadow  of  the  ring  on  the  planet,  were  succes- 
sively made,  as  the  powers  of  the  telescope  were  improved. 
During  the  present  century  many  astronomers  assert  the 
multiple  division  of  the  rings  of  Saturn,  and  the  evidence 
is  so  conclusive,  that  the  existence  of  dark  lines,  concentric 
with  the  rings,  (and  like  that  which  severs  the  two  prin- 
cipal rings,  cannot  be  denied,)  though  there  is  every  rea- 
son to  believe  that  these  lines  are  only  to  be  seen  oc- 
casionally. With  the  full  power  of  the  refractor  of  the 
Cincinnati  Observatory,  defining  in  the  most  beautiful 
manner  all  the  other  delicate  characteristics  of  Saturn 
and  his  rings,  I  have  never  been  able  to  perceive  any 
trace  of  any  other  than  the  principal  division. 

The  bright  and  dark  belts  and  certain  spots,  which 
mark  both  the  surface  of  the  planet  and  the  ring,  have 
furnished  the  means  of  fixing  the  period  of  rotation  of 
the  planet  on  its  axis  at  lOh.  29m.  16.8s.,  while  the  ring 
revolves  on  an  axis  nearly  coincident  with  that  of  the 
planet  in  lOh.  32m.  15s. 

If  we  reflect  on  the  structure  and  position  of  Saturn's 
rings,  the  phenomena  attending  its  disappearance  and 
reappearance  become  readily  explicable.  The  plane  of 
the  ring  produced  indefinitely,  intersects  the  plane  of  the 
earth's  orbit  in  a  straight  line.  This  is  called  the  line 
of  nodes  of  the  ring.  This  line  of  nodes,  remaining 
nearly  parallel  to  itself,  will  manifestly  move  as  the  ring 
moves,  carried  with  the  planet  in  its  revolution  round  the 
sun.  During  one-half  of  Saturn's  revolution  in  its  orbit 
the  sun  will  illumine  the  northern  side  of  the  rings, 
during  the  other  half  it  will  shine  on  the  southern  side. 


SATURN  .  CINCINNATI  OBS. 


SATURN.  161 

Thus  the  ring,  carried  by  the  planet,  will  finally  come 
into  a  position  such  that  the  sunlight  will  fall  on  neither 
side,  but  on  the  edge  of  the  ring  only,  and  when  in  this 
position  it  is  manifest  that  the  plane  of  the  ring  passes 
through  the  sun.  If,  when  in  this  position,  the  earth 
comes  between  Saturn  and  the  sun,  a  spectator  from  the 
earth's  surface  will  behold  the  edge  of  the  ring,  if  visible 
at  all,  as  a  delicate  line  of  light  extending  beyond  the 
disk  of  the  planet,  and  passing  through  its  center. 

The  earth,  moving  forward  in  its  orbit  from  opposi- 
tion of  the  planet,  will  pass  through  the  plane  of  the 
ring,  and  upon  the  non-illuminated  side.  As  Saturn 
moves  very  slowly  in  comparison  with  the  earth,  while 
the  plane  of  the  ring  is  sweeping  from  the  one  side  of  the 
sun  to  the  other,  the  earth  may  pass  more  than  once 
through  the  plane  of  the  ring,  repeating,  in  some  sense, 
the  phenomenon  of  disappearance.  As  Saturn's  period 
of  revolution  extends  to  nearly  thirty  of  our  years,  during 
one- half  of  this  period  the  inhabitants  of  the  earth  will 
behold  one  side  of  the  ring,  and  during  the  other  half 
they  will  look  upon  its  opposite  surface.  All  the  changes 
from  the  greatest  opening  of  the  ring,  when  the  planet  is 
seen  like  a  magnificent  golden  ball,  engirdled  by  its  ring 
of  golden  light,  down  to  the  total  disappearance  of  the 
ring,  require  about  fifteen  years.  Then  the  reverse 
changes  occur,  and  all  the  phases  and  transmutations  are 
accomplished  in  about  thirty  years,  when  they  are  again 
repeated  in  the  same  order. 

The  disappearance  of  the  ring,  which  took  place  in 
1848,  was  watched  by  the  author  at  the  Cincinnati  Ob- 
servatory with  the  powerful  refractor  of  that  institution. 
A  minute  fibre  of  light  remained  clearly  visible  even 
when  the  edge  of  the  ring  was  turned  directly  to  the 


162  SATUKN. 

eye  of  the  spectator.  The  delicacy  of  this  line  far  ex- 
ceeds anything  ever  before  witnessed.  When  compared 
with  the  finest  spider's  web  stretched  across  the  field  of 
view,  the  latter  appeared  like  a  cable,  so  greatly  did  it 
surpass  in  magnitude  the  filament  of  light  presented  in 
the  edge  of  Saturn's  ring.  I  had  the  pleasure  of  witness- 
ing the  phenomena  so  beautifully  described  by  Sir  Wil- 
liam Herschel,  the  movement  of  the  satellites  along  this 
line  of  light,  "  like  golden  beads  on  a  wire."  This  is  a 
consequence  of  the  coincidence  of  the  planes  of  the  orbits 
of  these  satellites  with  the  plane  of  the  ring ;  hence,  when 
the  ring  is  seen  edgeways,  these  orbits  will,  in  like  man- 
ner, be  seen  as  straight  lines,  coincident  with  the  line 
under  which  the  ring  is  seen. 

To  add  to  the  extraordinary  constitution  of  this  wonder- 
ful planet,  another  ring  has  recently  been  discovered  by 
Bond,  of  Cambridge,  and  by  Lassell,  of  Liverpool,  more 
mysterious,  if  possible,  than  those  previously  known. 
This  ring  lies  between  the  planet  and  the  bright  ring, 
and  is  of  a  dusky  hue,  and  only  discernible  in  powerful 
telescopes.  Its  outline  is  thex  same  as  that  of  the  other 
rings,  with  the  inner  edge  of  the  smaller  of  which  it 
seems  to  unite.  This  extraordinary  appendage  is  so  conr 
stituted  as  to  reflect  but  little  light,  and  is  sufficiently 
translucent  to  permit  the  body,  of  the  planet  to  be  seen 
through  its  substance.  I  have  frequently  examined  this 
dusky  ring  with  the  Cincinnati  refractor,  and  have  some- 
times been  confident  that  its  breadth  at  the  extremities  of 
its  longer  axis  was  much  greater  than  that  which  would 
be  due  to  an  elliptical  figure  concentric  with  the  bright 
rings. 

Knowing,  as  we  do,  the  distance  of  Saturn,  it  is  easy, 
from  the  measures  of  the  diameter  of  his  surrounding 


SATURN.  163 

rings,  to  compute  their  absolute  dimensions.  .The  ex- 
terior diameter  of  the  larger  ring  is  no  less  than  176,418 
miles,  and  its  breadth  is  21,146  miles.  The  exterior 
diameter  of  the  second  ring  is  157,690  miles,  leaving  a 
chasm  between  the  bright  rings  of  1,791  miles  across. 
The  breadth  of  the  second  ring  is  34,351  miles  and  the 
interval  between  the  pknet  and  this  ring  is  19,090. 
miles.  The  thickness  of  the  rings  is  a  matter  of  con- 
jecture, as  it  is  too  minute  a  quantity  to  be  obtained  by 
any  means  of  measurement  at  present  within  our  reach. 
Sir  John  Herschell  does  not  believe  it  can  exceed  250 
miles.  A  single  second  of  arc,  at  a  distance  equal  to  Sa- 
turn, subtends  nearly  5,000  miles ;  so  that  a  bright  globe 
of  5,000  miles  in  diameter,  removed  to  Saturn's  distance, 
would  be  covered  by  the  smallest  spider's  web  stretched 
across  fhe  field  of  view  of  the  eye-piece  of  the  telescope. 
In  case  we  admit  the  rings  of  Saturn  to  be  250  miles  in 
thickness,  then,  when  seen  edgeways,  the  filament  of  b'ght 
seen  reflected  from  the  outer  circumference  is  only  one- 
twentieth  part  the  diameter  of  the  spider's  web. 

We  pass  now  to  an  examination  of  the 

SATELLITES  OF  SATURN. — The  largest  of  these  satel- 
lites was  discovered  by  Huygens  as  early  as  1665.  Four 
others  were  discovered  some  thirty  years  later  by  Cassini. 
Two  more  were  added  by  Sir  William  Herschel  on  the 
completion  and  application  of  his  grand  reflector  in  1789, 
while  an  eighth  satellite  was  discovered  by  two  observers, 
Bond  and  Lassell,  on  the  same  night  (Sept.  19th,  1848), 
the  one  in  Cambridge,  United  States,  the  other  in  Liver- 
pool, England.  We  have  thus,  in  addition  to  the  anom- 
alous rings  which  surround  Saturn,  a  scheme  of  no 
less  than  eight  dependent  worlds,  all  of  which  revolve 
about  the  central  orb  in  elliptical  curves,  and  in  periods 


164  SATURN. 

varying  from  twenty-two  hours  to  seventy-nine  days. 
If  the  celestial  scenery  of  Jupiter  is  rendered  magnificent 
by  the  splendor  of  his  four  moons,  what  must  be  the 
amazing  grandeur  of  the  nocturnal  sky  of  Saturn,  arched 
from  horizon  to  horizon  by  his  broad,  luminous  girdle 
(on  which  the  shadow  of  the  planet,  like  the  dark  hand 
of  a  mighty  dial,  will  mark  the  hours  of  the  night),  the 
changes,  phases,  eclipses,  the  occultations  of  his  numer- 
ous moons,  and  the  "brilliant  background  of  glittering 
constellations  which  gem  our  nocturnal  sky,  must  alto- 
gether form  a  display  of  celestial  splendor  of  which  the 
human  mind  can  form  but  a  faint  conception. 

In  consequence  of  the  vast  distance  at  which  the  Sa- 
turnian  system  is  removed,  and  the  magnitude  and  power 
of  the  telescope  demanded  for  its  examination,  we  are 
as  yet  comparatively  ignorant  of  many  facts,  wljich,  in 
the  case  of  Jupiter's  moons,  have  been  well  determined. 
It  will  be  remembered  that  the  moon's  distance  from  the 
earth  is  about  237,000  miles.  Three  of  Saturn's  moons 
fall  far  within  this  limit,  and  the  fourth  is  but  243,000 
miles  from  its  primary.  The  fifth  is  340,000  miles  dis- 
tant ;  the  sixth,  788,000  miles ;  the  seventh  (latest  dis- 
covered), is  about  1,000,000  miles  distant,  while  the 
eighth  is  removed  from  Saturn  to  a  distance  of  nearly 
2,300,000  miles. 

The  nearest  of  the  moons,  revolving  at  a  distance  of 
120,000  miles,  circulates  round  the  primary  in  about 
twenty-two  hours  and  a  half,  presenting  all  the  phases 
exhibited  by  our  moon,  in  less  than  a  thirtieth  part  of 
the  time.  Its  disk,  as  seen  from  Saturn,  will  surpass 
the  moon's  disk  in  the  ratio  of  ten  to  one.  Of  the  five 
earliest  discovered  satellites,  two  are  readily  seen  with 
any  good  telescope.  The  five  may  now  be  seen  by  many 


UNiV-r.SiT 

165 

refractors  and  reflectors  of  modern  construction,  while 
the  three  smallest  satellites  are  only  rendered  visible  by 
a  few  of  the  most  powerful  instruments  in  the  world. 

We  shall  here  close  what  we  have  to  present  of  the 
structure  of  the  Saturnian  system.  We  have  thus  ter- 
minated the  examination  of  all  planetary  bodies  known 
to  the  ancients,  and  have  added  to  these  the  new  objects 
revealed  by  the  telescope,  inclosed  by  the  circumscrib- 
ing orbit  of  Saturn.  Within  these  limits  we  find  all  the 
phenomena  known  to  the  master  minds  to  whom  we  are 
indebted  for  the  vast  extension  of  the  boundaries  of 
human  knowledge  in  the  solar  system. 

Before  we  pass  these  old  limits,  which  for  so  many 
thousand  years  were  regarded  as  impassable,  we  must 
render  an  account  of  the  great  discoveries,  whereby  it 
became  possible  to  achieve  the  crowning  victories  of 
human  genius  in  the  planetary  regions,  and  to  extend 
these  conquests  far  beyond  the  limits  of  solar  influence 
into  regions  of  space  and  among  revolving  orbs,  of  which 
the  old  philosophers  had  no  conception. 


CHAPTER    IX. 


THE  LAWS   OF  MOTION  AND   GRAVITATION. 


Tmt  DEMANDS  OP  FORMAL  ASTRONOMY.— THOSE  OF  PHYSICAL  ASTRONOMY.— 
SYNOPSIS  OK  THE  DISCOVERIES  ALREADY  MADE.— QUESTIONS  REMAINING  TO  BB 
ANSWERED. — INQUIRY  INTO  CAUSES. — THE  LAWS  OF  MOTION  DEMANDED. — 
RECTILINEAL  MOTION.— FALLING  BODIES. — LAW  OF  DESCENT. — MOTION  OF 
PROJECTILES. — CURVILINEAR  MOTION. — FIRST  LAW  OF  MOTION. — SECOND 
LAW  qp  MOTION.— MOMENTUM  OF  MOVING  BODIES.— MOTION  ON  AN  INCLINED 
PLANE.— THE  CENTRIFUGAL  FORCE.— CENTRAL  ATTRACTION.— GRAVITATION. 
—LAWS  OF  MOTION  APPLIED  TO  THE  PLANETS.— QUESTIONS  PROPOUNDED  IN 
PHYSICAL  ASTRONOMY.— NEWTON'S  ORDER  OF  INVESTIGATION.— His  ASSUMED 
LAW  OF  GRAVITATION. — OUTLINE  OF  HIS  DEMONSTRATION. — ITS  IMPORTANCB 
AND  CONSEQUENCES. — THE  LAW  OF  GRAVITATION  EMBRACKS  ALL  THE  PLAN 
BTS  AND  THEIR  SATELLITES. — GRAVITATION  BESIDES  IN  EVERY  PARTf  ">LE  Of 
MATTER. 


THE  discoveries  thus  far  made  among  the  revolving 
worlds  dependent  on  the  sun  have  their  origin  in  a 
rigorous  comparison  between  the  actual  phenomena  pre- 
sented in  nature  and  the  hypothetical  facts  derived  from 
an  assumed  theory.  Hipparchus  and  Ptolemy  surpassed 
their  predecessors  because,  on  careful  examination,  they 
discovered  that  the  motion  of  the  sun  and  moon  and 
planets,  not  being  uniform,  as  had  been  asserted  and  be- 
lieved, they  explained  this  irregularity  by  the  hypothe- 
sis of  an  eccentric  position  in  the  central  orb,  thus 
enabling  them  to  anticipate  all  the  anomalous  movements 
known  in  the  age  in  which  they  lived.  Succeeding  dis- 
coveries, adding  to  the  complexity  of  the  theory  of  eccen- 
trics and  epicycles,  drove  Copernicus  to  a  neir  center  of 


MOTION     AND    GRAVITATION.          167 

motion  in  the  sun,  and  this  hypothesis,  united  to  the  old 
theory  of  epicycles,  was  sufficient  to  harmonize  the  then 
known  facts  of  astronomy  with  the  predictions  of  scien- 
tific men. 

Increased  accuracy  of  observation,  however,  soon  re- 
vealed certain  undoubted  discrepancies  between  the  abso- 
lute places  of  the  heavenly  bodies,  as  given  by  ^instru- 
mental observation,  and  their  places  as  obtained  by 
computation,  and  after  exhausting  every  possible  expe- 
dient to  restore  harmony  between  observation  and  com- 
putation, finding  it  impossible,  Kepler,  as  we  have  seen, 
was  compelled  to  abandon  the  circular  theory,  as  Coper- 
nicus before  him  had  been  forced  to  relinquish  the  geo- 
centric hypothesis. 

In  all  this  long  lapse  of  many  thousands  of  years  the 
human  mind  has  occupied  itself  exclusively  with  the 
great  problem  of  framing  an  hypothesis  which  would  em- 
brace all  the  phenomena  as  presented  in  the  heavens 
It  was  a  question  as  to  where  was  the  center  of  motion, 
not  why  it  was  there ;  what  was  the  figure  of  the  plane 
tary  orbits,  not  why  this  particular  figure  existed ;  how 
the  planets  deviated  from  a  uniform  velocity  in  their  rev- 
olution round  the  sun,  not  why  they  were  accelerated 
and  retarded ;  how  the  periods  of  revolution  and  the 
mean  distances  were  related,  not  why  they  were  thus  re- 
lated. In  short,  the  facts  and  not  the  causes  occupied 
the  exclusive  attention  of  the  great  astronomers,  until  the 
science  of  facts,  or  formal  astronomy,  had  reached  its 
limit,  and  the  mind,  having  exhausted  this  field  of  in- 
vestigation, was  compelled  to  turn  its  attention  to  causes 
or  to  physical  astronomy. 

Let  us  review  and  condense  the  facts  thus  far  de- 
veloped by  formal  astronomy. 


168  THE     LAWS     OF 

The  planets  revolve  about  the  sun  as  their  common 
center  of  motion  in  orbits  whose  figure  is  nearly,  if  not 
quite,  elliptical. 

Their  motion  is  not  uniform,  but  grows  swifter  as  they 
approach  the  sun,  and  loses  in  velocity  after  passing  their 
perihelion  or  nearest  point  to  the  sun. 

The  dimensions  of  the  planetary  orbits  are  not  abso- 
lutely invariable.  There  are  slight  fluctuations  not  to  be 
overlooked  in  the  periodic  times  and  mean  distances. 

The  positions  of  the  orbits  in  their  own  plane  are  sub- 
ject to  perpetual  change,  very  slow  in  some  of  the  planets, 
but  comparatively  rapid  in  the  moon  and  in  the  satellites 
of  other  planets. 

The  inclinations  of  the  planes  of  the  planetary  orbits 
to  a  fixed  plane  are  also  in  a  state  of  fluctuation,  some 
angles  increasing  while  others  are  diminishing. 

The  lines  of  nodes,  in  which  the  planes  of  the  orbits  of 
the  planets  intersect  the  plane  of  the  earth's  orbit,  are 
not  fixed  lines.  They  are  found,  on  the  whole,  to  retro- 
grade, but  are  sometimes  found  to  advance  in  the  order 
of  planetary  revolution. 

The  moon  exhibits  anomalous  movements,  very  marked 
and  well-defined,  and  which  are  evidently  outside  of  her 
elliptic  motion,  rising  above  and  superior  to  the  general 
law  of  her  revolution. 

*The  most  considerable  of  these  lunar  inequalities 
amounts  to  1°  20'  30'',  by  which  quantity  she  is  alter- 
nately in  advance  and  behind  her  elliptic  place  in  her 
orbit.  This  motion  was  known  to  the  ancients,  having 
been  discovered  by  Ptolemy,  and  was  readily  appreciable 
by  the  imperfect  instruments  employed  by  the  Greek  as- 
tronomers. It  is  known  as  the  moon's  evection. 

A.  second  inequality,  amounting  to  1°  4',    called  the 


MOTION     AND     GRAVITATION.         169 

moon's  variation,  was  discovered  bj  the  Arabians,  and 
by  them  transmitted  to  posterity,  showing  the  moon's 
motion  accelerated  in  the  quadrants  of  her  orbit  preced- 
ing her  conjunctions  and  oppositions,  and  retarded  in  the 
alternate  quadrants. 

A  third  lunar  inequality  was  called  the  annual  equa- 
tion, a  name  adopted  to  express  the  fact  that  the  moon's 
place  in  her  orbit  is  for  half  a  year  in  advance  of  her 
elliptic  place,  and  for  the  other  half  year  behind  it. 

The  line  of  apsides  or  longer  axis  of  the  lunar  orbit 
performs  a  complete  revolution  in  the  heavens  in  3232.57 
days. 

The  line  of  nodes  revolves  round  the  heavens  in 
6793.39  days. 

The  vernal  equinox  is  also  in  motion,  sweeping  round 
the  heavens  in  25.868  years,  while  the  north  pole  of  the 
heavens  revolves  round  the  pole  of  the  ecliptic  in  the 
same  exact  period. 

Add  to  these  facts,  all  discovered  by  observation  and 
reflection,  the  grand  discovery  of  Kepler,  that  the  squares 
of  the  periods  of  revolution  are  precisely  proportional  to 
the  cubes  of  the  mean  distances  of  the  planets,  and  that 
this  and  the  other  laws  of  Kepler  govern  the  satellites, 
and  we  have  a  fair  exhibition  of  the  great  truths  of  formal 
astronomy,  and  it  is  to  answer  why  these  phenomena 
exist  that  physical  astronomy  has  been  cultivated  as»  a 
science. 

Why  does  a  planet  continue  to  revolve  about  the  sun  ? 
In  case  it  approach  the  sun  at  all,  why  not  continue  that 
approach  until  it  be  precipitated  on  the  surface  of  the 
solar  orb  ?  Why  do  these  revolving  bodies  describe  el- 
liptic orbits,  with  the  sun  always  in  the  focus  of  every 
orbit?  Why  are  the  deviations  from  elliptic  motion 

8 


170  THE     LAWS     OF 

what  they  are  ?  and  how  comes  it  that  the  elliptic  ele- 
ments are  in  a  state  of  perpetual  fluctuation  ?  Why  dc 
not  the  planets  fall  on  the  sun,  or  fly  off  into  space,  or 
stop  motionless  in  their  orbits  ?  What  holds  the  earth  to 
the  sun,  or  the  moon  to  the  earth,  so  that  they  never 
part  company,  and  unitedly  sweep  harmoniously  round 
the  sun  ?  What  bond  unites  all  the  satellites  to  their 
primaries,  and  all  these  primaries  to  one  central  orb  ? 

Do  all  these  interrogatories  admit  of  a  single  answer, 
or  shall  we  find  these  phenomena  to  spring  from  diverse 
origins,  and  due  to  a  variety  of  causes  ? 

Before  it  was  possible  to  consider  any  one  of  these 
grand  problems  it  became  necessary  to  reconstruct  the 
old  science  of  mechanics  or  mechanical  philosophy,  which 
was  contemporaneous  with  the  Greek  astronomy  of 
Ptolemy,  and  at  the  time  of  Kepler  and  Galileo  exerted 
quite  as  powerful  an  influence  over  the  human  mind  as 
did  the  doctrines  of  Ptolemy  and  Hipparchus.  The  phil- 
osophy of  Aristotle  was  taught  in  all  the  schools,  sus- 
tained by  the  immense  influence  of  professional  organiza- 
tion, and  received  with  a  fullness  of  confidence  and  depth 
of  submission  which,  so  far  from  tolerating  doubt,  actually 
prohibited  inquiry. 

As  the  planets  and  their  satellites  were  bodies  in  mo- 
tion, no  advance  could  be  made  in  the  inquiry  concern- 
ing causes  until  the  true  nature  of  motion  and  the  laws 
by  which  it  was  governed  could  be  determined.  These 
laws  could  only  be  revealed  by  accurate  thought  and  ob- 
servation, and  would  naturally  be  independent  of  the 
cause  producing  the  motion. 

The  most  obvious  example  of  motion  is  where  a  heavy 
body  is  dropped  vertically  from  any  height,  and  falls 
toward  the  earth.  Observation  teaches  the  rectilineal  path 


MOTION     AND     GRAVITATION.  171 

of  such  a  falling  body,  as  well  as  its  direction t  which  is 
toward  the  center  of  the  earth.  It  was  a  matter  of  ex- 
periment to  determine  whether  the  velocity  tfata  uniform 
or  accelerated,  and  if  accelerated,  observatic  i  alone  could 
determine  the  law  of  acceleration  All  th«  TIM  quite  in- 
dependent of  the  cause  producing  the  origin  1  motion,  the 
rectilineal  direction,  the  acceleration,  and  the  direction 
toward  the  earth's  center. 

Aristotle  had  laid  down  the  law  of  fall  *g  bodies,  and 
asserted  that  in  case  balls  of  unequal  wei  ht  were  drop- 
ped at  the  same  moment  from  equal  elevati  ns  the  heavier 
ball  would  move  the  swifter,  and  that  the  relocity  of  the 
two  balls  would  be  directly  proportional  tx  their  respect- 
ive weights.  It  was  easy  by  experiment  ;>  prove  or  dis- 
prove this  statement,  and  Galileo  is  said  to  have  given 
the  first  powerful  blow  to  the  Greek  philosophy,  by 
showing  experimentally,  (by  dropping  lalls  of  unequal 
weights  from  the  summit  of  the  leaning  tower  of  Pisa,) 
that  the  velocity  of  the  ball,  or  the  time  occupied  in  the 
fall,  was  entirely  independent  of  the  weight  of  the 
ball,  the  resistance  of  the  atmosphere  being  taken  into 
account. 

By  measuring  the  space  passed  over  by  a  falling  body 
in  equal  intervals  of  time,  it  became  possible  to  deter- 
mine the  law  of  descent,  and  it  was  thus  found  that  every 
falling  body  passes  through,  say,  sixteen  feet  in  the  first 
second  of  its  fall.  This  is  the  velocity  impressed  in  the 
first  second  of  time,  and  were  the  body  to  move  on  with 
the  velocity  thus  acquired,  it  would  pass  uniformly  over 
thirty-two  feet  in  the  next  second  of  time.  But  it  is 
found  that  the  velocity  of  every  falling  body  is  increasd 
in  every  second  of  time  by  the  same  precise  velocity 
acquired  in  the  first  second,  and  thus  in  case  a  cannon 


172  THE     LAWS     OF 

ball  were  projected  downward  at  the  rate  of  a  thousand 
feet  in  one  second,  it  would  not  only  pass  over  one 
thousand  feet,  but  the  sixteen  additional  feet  acquired  by 
a  body  falling  from  a  state  of  rest  would  be  added  to 
the  thousand  feet  due  to  the  impulsive  force  of  the  gun- 
powder. 

Again,  in  projecting  a  body  vertically  upward,  it  was 
discovered  by  experiment  tlrnt  at  equal  elevations  in  the 
ascent  and  descent  the  velocities  were  identical,  and  thus 
whatever  might  be  the  cause  retarding  the  ascending 
body,  or  accelerating  the  descending  one,  that  cause  was 
found  to  exert  its  force  with  a  constant  energy. 

Galileo  was  the  first  fully  to  develop  the  facts  above 
stated,  which  facts  manifestly  began  to  couple  motion  and 
velocity  with  some  mysterious  cause  of  acceleration  and 
retardation. 

The  rectilineal  motion  of  falling  bodies  naturally  led 
to  the  inquiry  as  to  the  line  in  which  a  body,  receiving  a 
single  impulse,  would  move,  if  entirely  free  from  the  influ- 
ence of  extraneous  forces.  A  body  shot  from  a  gun  hori- 
zontally, at  the  commencement  of  its  motion  seemed  to 
move  in  a  right  line,  but  a  more  rigid  examination 
showed  that  (the  air  as  a  resisting  medium  out  of  con- 
sideration) the  bullet  commenced  to  fall  at  the  moment 
of  its  flight,  and  actually  did  fall  in  one  second  of  time 
through  a  vertical  height  precisely  equal  to  the  space  it 
would  have  fallen  through  if  dropped  from  the  muzzle  of 
the  gun.  Here,  then,  was  a  deviation  from  a  rectilineal 
path  accounted  for  by  admitting  a  constant  deflecting 
force  precisely  equal  to  that  force,  wherever  it  may  be 
lodged,  or  whatever  it  may  be,  which  produces  and  ac- 
celerates the  velocity  of  falling  bodies. 

As  the  right  line  is  the  most  perfect  of  all  lines,  and 


MOTION     AND     GRAVITATION.  173 

as  uniform  motion  in  a  right  line  is  the  simplest  of  all 
motions,  Galileo  conceived  the  idea  that  in  case  a  body 
receive  a  single  impulse  giving  a  velocity  of  any  rate  per 
second,  that  the  body  thus  set  in  motion  will  move  off 
with  uniform  velocity  in  a  straight  line,  holding  the  di- 
rection in  which  the  impulse  is  applied,  and  will  thus  con- 
tinue moving  for  ever,  unless  some  force  or  power 
be  exerted  to  change  the  direction  or  to  destroy  the 
velocity. 

This  conception  or  hypothesis  could  not  be  proved 
directly  from  experiment.  A  ball  perfectly  hard,  round 
and  smooth,  shot  on  a  level  surface  like  ice,  would  pre- 
serve its  rectilineal  path  and  its  initial  velocity  much 
longer  than  if  opposed  by  irregularities  of  surface  and 
other  resisting  causes  ;  and  thus  it  became  manifest  that 
as  the  resistances  to  motion  were  diminished,  there  was  a 
nearer  positive  and  experimental  approach  to  the  verifica- 
tion of  the  principle  laid  down  by  Galileo,  till  finally  it 
became  a  settled  principle,  and  was  at  length  dignified  as 
the  first  great  law  of  motion. 

Previous  to  the  discovery  of  this  law  the  mind  had 
never  been  able  to  conceive  the  idea  that  motion  could 
continue  after  the  cause  producing  it  had  ceased  to  act, 
and  yet  there  is  no  motion  produced  by  human  contriv- 
ance, such  as  the  motion  of  a  stone  from  a  sling,  or  a 
ball  from  a  cannon,  in  which  it  is  not  manifest  that  the 
force  producing  the  motion  ceases  its  action  after  the  first 
impulse.  The  sling  cannot  pursue  the  stone  once  liber- 
ated, nor  the  powder  with  its  expansive  power  follow  the 
ball  once  released  from  the  gun  ;  and  thus  it  is  clear  that 
motion,  once  generated,  survives  for  a  longer  or  shorter 
time  the  direct  action  of  the  impulsive  force. 

So  much  for  rectilineal  motion.     We  are  indebted  to 


174  THE     LAWS     OF 

Galileo  again  for  the  second  law  of  motion,  or  the  law 
by  which  we  pass  from  rectilineal  to  curvilinear  motion. 
A  ball  projected  horizontally,  as  we  have  seen,  soon  com- 
menced to  fall  away  from  the  straight  line  in  which  its 
motion  commenced.  Galileo  proved  that  under  the 
united  effect  of  the  projectile  force,  and  the  force  which 
caused  it  to  fall  toward  the  earth,  the  ball  would  de- 
scribe a  regular  curve,  called  a  parabola,  which  is  nothing 
more  than  an  ellipse,  whose  major  axis  is  infinitely  long. 
This  curve  may  be  seen  in  the  form  of  the  jet,  when 
water  or  any  other  fluid  spouts  from  an  orifice  near  the 
bottom  of  a  cylindrical  vessel. 

The  Florentine  philosopher  in  pursuing  this  subject 
finally  came  to  generalize  the  principle  involved,  and  dis- 
covered that  if  a  body  in  motion  at  any  given  rate  re- 
ceive an  impulse,  whose  line  of  direction  forms  any  angle 
'  with  the  line  of  direction  of  the  moving  body,  it  will  im- 
mediately take  up  a  new  line  of  direction,  according  to  a 
law  which  may  be  thus  announced : — 

If  two  sides  of  a  square  or  rectangle  represent  the 
intensities  and  directions  of  two  impulsive  forces 
acting  at  the  same  instant,  on  a  body  at  the  angle 
formed  by  these  sides,  then  the  body  which,  at  the 
end  of  one  second,  would  have  been  found,  under  the 
impulse  of  either  force,  at  the  extremity  of  the  side 
representing  the  force,  will  neither  follow  the  one  side 
of  the  rectangle  nor  the  other,  but  will  take  the  direc- 
tion of  the  diagonal,  and  at  the  end  of  one  second  will 
be  found  at  the  extremity  of  that  diagonal,  as  may  be 
more  readily  comprehended  from  the  figures  below. 

Let  F  be  any  impulsive  force,  such,  that  acting  on  the 
material  point  P,  in  the  direction  P  B,  would  project  it 
to  B  in  one  second  of  time,  and  F'  be  an  impulsive  force 


MOTION     AND     GRAVITATION.         175 

which,  acting  on  the  same  material  point  P,  in  the  direc- 
tion P  A,  would  project  it  to  A  in  one  second ;  then,  in 
case  the  two  forces  operate  at  the  same  moment  on  the 
material  point  P,  at  the  end  of  one  second  it  will  neither 
be  found  at  B  nor  at  A,  but  will  be  found  at  C,  the  ex- 
tremity of  the  diagonal  of  the  parallelogram. 


£  C 

This  principle  is  known  as  the  second  law  of  motion, 
and  is  also  known  as  the  parallelogram  of  forces. 

In  these  investigations  no  account  has  been  taken  of 
the  weight  or  mass  of  the  body  moved.  It  was  clearly 
perceived  that  the  force  exerted  by  a  body  at  rest  press- 
ing upon  any  support  was  precisely  proportioned  to  its 
weight,  and  hence  a  ball  weighing  ten  pounds  would 
bend  a  spring  through  ten  times  the  space  due  to  a  ball 
weighing  but  one  pound.  Aristotle  knowing  this  truth, 
and  believing  that  this  pressure  downward  was  the  mov- 
ing force,  when  a  body  fell  freely,  asserted  the  principle 
that  a  body  would  fall  with  a  velocity  proportioned  to  its 
weight,  which,  as  we  have  said,  was  disproved  by  Galileo 
in  his  celebrated  experiment  at  the  leaning  tower  of  Pisa. 

It  was  manifest,  however,  that  when  two  balls  of  un- 
equal weight  fell  from  the  same  elevation,  although  they 
struck  the  ground  at  the  same  moment,  or  fell  with  equal 
velocities,  the  effect  of  the  blow  struck  by  the  heavy 
body  was  very  different  from  that  produced  by  the  lighter 


176  THE     LAWS     OF 

body.  Indeed,  it  was  easy,  by  experiment,  to  prove 
the  effect  was  precisely  proportioned  to  the  weight  of  the 
falling  body,  and  that  a  body  of  ten  pounds  weight  would 
strike  a  blow  ten  times  more  powerful  than  a  one  pound 
weight  after  falling  through  equal  heights.  It.  was  thus 
s^en  that  to  estimate  the  effect  of  a  blow  struck  by  a 
moving  body  we  must  take  into  account  not  only  the 
velocity  but  also  the  weight  or  mass  of  the  body.  The 
same  body,  with  double  velocity,  doubling  its  effect,  in 
short,  the  mass  multiplied  by  the  velocity,  now  called, 
the  momentum,  became  the  true  representative  of  the 
effect  produced  by  the  blow  struck  by  a  moving  body. 

Having  reached  clear  ideas  and  true  laws  on  these  im- 
portant subjects,  Galileo  gave  his  attention  to  the  circum- 
stances of  motion  on  an  inclined  plane.  By  experiment 
he  demonstrated  that,  if  the  same  body  roll  down  planes 
of  tke  same  vertical  height,  but  with  different  inclinations, 
the  velocity  acquired  on  reaching  the  foot  of  any  one  of 
these  planes  will  be  independent  of  the  inclination,  and 
will  always  be  equal  to  the  velocity  due  to  the  verti- 
cal height  of  the  inclined  plane.  This  discovery  presented 
the  principle  of  the  third  and  last  law  of  motion,  and, 
after  much  discussion,  came  to  be  adopted  as  a  funda- 
mental truth  in  mechanical  science.  These  laws  of  mo- 
tion were  the  result  of  clear  reasoning,  based  upon 
accurately  conducted  experiment,  and  were  quite  inde- 
pendent of  the  actual  causes  producing  motion. 

So  soon  as  the  knowledge  of  the  second  law  of  motion 
was  attained,  whereby  it  became  demonstrable  that  a  body 
set  in  motion  by  a  single  impulse,  and  then  operated  on 
by  a  constant  power,  would  describe  a  curve,  it  seems 
strange  to  us,  surrounded  as  we  now  are  by  the  full  illumi- 
nation of  a  true  science,  that  this  principle  was  not  directly 


MOTION     AND     GRAVITATION.         177 

applied  to  account  for  the  motions  of  revolution  of  the 
celestial  orbs. 

Kepler,  whose  fertile  genius,  ever  active  and  untiring, 
sought  the  cause  of  planetary  motion,  being  ignorant  of 
the  laws  of  motion,  felt  that  he  must  discover  and  reveal 
some  constantly  active  power  operating  in  the  direction 
of  the  planetary  motion  so  as  to  keep  up  the  velocity, 
believing  that  without  some  such  ever-active  force  the 
planets  must  of  necessity  stop.  The  successors  of  Kepler 
^and  of  Galileo,  for  fifty  years,  or  during  the  first  half  of 
the  seventeenth  century,  felt  strongly  the  necessity  of  a 
physical  theory  of  the  planetary  motions,  without  attain- 
ing to  anything  clear  or  satisfactory. 

That  all  heavy  bodies  were  in  some  way  attracted  by 
the  earth,  and  that  the  center  of  attraction  was  in  the 
earth's  center,  was  manifest  from  the  fact  that  every  body 
falling  freely,  sought  the  earth's  center.  But  how  a 
central  force,  lodged  in  the  earth  or  in  the  sun,  could 
operate  to  keep  up  a  motion  of  revolution  round  that 
center,  in  distant  bodies,  was  the  inexplicable  mystery. 
The  ancients  had  already  remarked  that  when  a  stone 
in  a  sling  is  whirled  rapidly  round  the  head  of  the 
slinger,  a  force  is  developed  which  powerfully  stretches 
the  string  by  which  the  stone  is  held.  This  force  was 
called  the  centrifugal  force,  and  it  finally  came  to  be  ac- 
cepted that,  in  all  revolving  bodies,  this  tendency  to  fly 
from  the  center  must  be  generated,  and  hence  in  the 
planets  and  their  satellites  a  like  tendency  must  exist. 
Reasoning,  then,  upon  the  two  great  facts,  that  all  bodies 
gravitate  to  the  earth,  and  from  analogy  all  bodies 
equally  gravitate  to  the  sun,  and  that  all  revolving 
bodies,  by  the  action  of  the  centrifugal  force  generated 
in  their  revolution,  are  disposed  to  fly  from  the  center 


178  THE     LAWS     OF 

of  motion,  Borrelli,  of  Florence,  in  1666,  seems  to  have 
been  the  first  to  conceive  the  idea  that  in  the  planets  and 
their  satellites  these  two  forces  might  mutually  destroy 
or  counterbalance  each  other,  and  leave  the  planet  in  a 
state  of  dynamical  equilibrium  to  pursue  its  journey  round 
the  sun. 

Here  we  find  the  germ  of  the  grand  theory  which  at  the 
present  day  embraces  within  its  grasp  the  entire  physical 
universe  of  God.  It  was,  however,  but  the  germ.  Borrelli 
did  not  pretend  to  demonstrate  the  truth  of  his  sugges- 
tion. To  accomplish  this,  it  became  necessary  to  demon- 
strate the  law  of  the  centrifugal  force  and  the  law  of 
gravitation,  and  then  to  show  that  the  first  of  these  forces, 
as  developed  by  the  velocity  of  revolution  of  any  planet, 
was  precisely  equal  to  the  force  of  gravitation  exerted  by 
the  sun  at  the  distance  to  which  the  planet  was  removed. 

The  law  governing  the  development  of  the  centrifugal 
force  could  be  investigated  experimentally.  A  cord  suf- 
ficiently strong  to  hold  a  body  suspended  from  a  fixed 
point  was  not  strong  enough  to  hold  the  same  body  when 
made  to  revolve  about  the  point,  and,  as  the  velocity  of 
revolution  was  increased,  the  strength  of  the  cord  had  to 
be  increased.  But  it  was  soon  found  that,  with  double 
the  velocity  a  cord  twice  as  strong  would  not  retain  the 
revolving  body.  The  centrifugal  force  increased,  there- 
fore, in  a  higher  ratio  than  the  simple  velocity.  By 
further  experiment  it  was  discovered  that  when  the  veloc- 
ity of  the  revolving  body  was  doubled,  the  cord  holding 
it  must  be  quadrupled,  and  when  the  velocity  was 
tripled  the  cord  must  be  made  nine-fold  stronger,  and 
hence  it  became  finally  a  fixed  principle  that  the  centri- 
fugal force  in  every  revolving  body  increased  with 
the  square  of  the  velocity.  It  remained  yet  to  ascertain 


MOTION     AND     GRAVITATION.         179 

in  what  way  this  force  was  affected  by  the  distance  of 
the  revolving  body  from  the  center  of  motion.  This  was 
accomplished  experimentally,  and  the  complete  law  regu- 
lating the  development  of  the  centrifugal  force  in  all  re- 
volving bodies  having  been  determined,  this  force  was 
found  to  increase  as  the  square  of  the  velocity  and  to  de- 
crease directly  as  the  distance  from  the  center  of  motion 
increased. 

With  the  knowledge  of  this  important  law,  we  can  re- 
turn to  the  consideration  of  the  planetary  revolutions. 
That  these  bodies  were  urged  directly  from  the  sun  by 
the  action  of  the  centrifugal  force  generated  by  their  ve- 
locity of  revolution  could  not  be  doubted,  and  to  counter- 
balance this  tendency  to  fly  from  the  center  of  motion 
some  force  precisely  equal  and  opposite  must  exist.  This 
force  was  called  the  gravitating  force,  or  force  of  grav- 
ity, and  the  law  regulating  its  intensity  remained  to  be 
discovered. 

Kepler  had  not  failed  to  conjecture  the  existence  of 
some  such  central  force  lodged  in  the  sun  and  in  the 
earth.  He  even  went  further,  and  conceived  the  same 
force  of  attraction  to  exist  in  the  moon,  and  finding  the 
tides  of  the  ocean  to  be  swayed  by  that  distant  orb,  he 
conceived  that  the  same  energy  which  manifested  itself 
in  a  heaving  up  of  the  ocean  wave,  must  exert  itself  with 
equal  power  on  the  solid  mass  of  the  earth.  These, 
however,  were  mere  speculations  with  Kepler,  and  even, 
in  case  he  had  seriously  undertaken  to  prosecute  the  re 
search,  the  ignorance  of  the  true  laws  of  motion  then 
existing  would  have  rendered  any  success  impossible. 
From  the  days  of  Kepler  to  those  of  Newton  this  great 
problem  constantly  occupied  the  thoughts  of  the  most 
eminent  philosophers :  Was  the  gravitating  force  whereby 


180  THE    LAWS    OP 

bodies  fell  to  the  earth's  surface  a  constant  or  variable 
force  ?  Was  this  force  operative  in  the  distant  regions 
of  space  ?  Did  its  power  extend  to  the  moon  ?  and  was 
it  there  precisely  what  it  should  be  in  order  to  counter- 
balance the  energy  of  the  centrifugal  force  ?  Did  this 
same  gravitating  power  dwell  in  the  sun  and  other  plan- 
ets, as  well  as  in  the  earth  ?  Did  the  sun's  gravity  ex- 
tend to  each  of  the  planets,  and  exert  at  these  different 
distances  an  energy  equal  and  opposite  to  the  existing 
centrifugal  force  due  to  the  planet's  distance  and  velo- 
city ?  In  short,  was  there  a  force  or  energy  dwelling  in 
every  particle  of  ponderable  matter  whereby  every  exist- 
ing particle  attracted  to  itself  every  other  existing  par- 
ticle, with  an  energy  proportioned  in  some  way  to  their 
weights  and  to  the  distances  by  which  they  were  separ- 
ated ?  Could  such  a  force,  lodged  centrally  in  the  sun, 
and  operating  by  any  law,  convert  the  rectilinear  motion 
of  a  body  darted  into  space  by  a  single  impulse  into  ellip- 
tical motion,  and  at  the  same  time,  at  every  point  in 
the  elliptical  orbit,  precisely  counterpoise  the  centrifugal 
force  due  to  the  planet's  distance  and  velocity?  Could 
the  same  force,  governed  by  the  same  laws  and  lodged  in 
the  primary  planets,  control  the  movements  of  their 
satellites  ?  These  were  the  grand  inquiries  which  en- 
grossed the  attention  of  the  generation  of  philosophers 
which  flourished  from  the  time  of  Kepler  and  Galileo  up 
to  the  era  rendered  immortal  by  the  grand  discovery  of 
the  law  of  universal  gravitation  by  Newton. 

NEWTON'S  DISCOVERY  OF  THE  LAW  OP  GRAVITATION. 
• — We  are  now  prepared  to  consider  the  train  of  reason- 
ing employed  by  the  English  philosopher  in  his  re- 
searches for  the  law  of  gravitation.  Many  astronomers 
before  Newton  had  conjectured  that  the  force  exerted  by 


MOTION    AND     GRAVITATION.  181 

4 

the  sun  on  the  planets,  and  by  the  primaries  on  Jheir 
satellites,  decreased  as  the  square  of  the  distance  in- 
creased, or  followed  the  law  of  the  inverse  ratio  of  tne 
square  of  the  distance.  This  was  inferred  from  the  con- 
sideration of  fact,  that  this  attractive  energy,  called  grav- 
ity, was  lodged  in  the  center  of  the  sun,  and  issued  from 
that  center  in  all  possible  directions,  like  light  emanating 
from  a  luminous  point.  As  the  distance  increased  from 
the  center  the  force  would  become  less  intense,  and  might 
follow  the  law  of  the  decrease  in  the  intensity  of  light, 
which  was  well  known  by  experiment  to  be  the  inverse 
ratio  of  the  square  of  the  distance.  It  was  one  thing  to 
conjecture  this  to  be  the  law  regulating  the  force  of  grav- 
ity, but  quite  a  different  thing  to  demonstrate  the  truth 
of  such  a  conjecture. 

The  investigation  as  pursued  by  Newton,  and  the  dis- 
coveries made  by  that  distinguished  philosopher,  followed 
progressively  in  a  series  of  distinct  propositions,  the  de- 
monstrations of  which  were  reached  at  different  periods. 

First,  Newton  demonstrated  that,  assuming  the  third 
law  of  Kepler  as  a  fact  derived  from  observation,  as  a 
consequence  of  this  fact,  (combined  with  the  law  of  the 
centrifugal  force,)  the  gravitation  of  the  planets  to  the  sun 
must  diminish  in  the  inverse  ratio  of  the  square  of  their 
respective  distances.  This  demonstration  was  accom- 
plished by  a  train  of  mathematical  reasoning,  of  which 
we  will  not  stop  to  give  any  account  at  present.  It  waa 
baaed,  however,  on  the  assumption  that  the  planetary 
orbits  were  circles,  and  hence  did  not  meet  the  case  of 
nature. 

The  second  step  was  to  prove  that  in  case  a  planet  re- 
volved in  an  elliptical  orbit,  that  at  every  point  of  its 
revolution  the  force  exerted  on  it  by  the  sun,  or  itfi 


182  THE     LAWS    OF 

% 

gravitation  to  tne  solar  orb,  was  always  in  the  inverse 
ratio  of  the  square  of  its  distance.  This  was  equivalent 
to  proving  that  if  a  body  in  space,  free  to  move,  received 
a  single  impulse,  and  at  the  same  moment  was  attracted 
to  a  fixed  center  by  a  force  which  diminished  as  the 
square  of  the  distance  at  which  it  operated  increased, 
such  a  body,  thus  deflected  from  its  rectilineal  path,  would 
describe  an  ellipse,  in  whose  focus  the  center  of  attrac- 
tion would  be  located. 

The  third  step  in  this  extraordinary  investigation  was 
to  demonstrate  that,  this  gravitating  power  lodged  in  the 
sun,  and  controlling  the  planetary  movements,  was  iden- 
tical with  that  force  exerted  by  the  earth  over  every  fall- 
ing body,  and  extending  itself  to  the  moon,  decreasing  in 
intensity  in  proportion  as  the  square  of  the  distance  in- 
creased, and  thus  opposing  itself  as  a  precise  equipoise 
at  every  moment  to  the  effect  of  the  centrifugal  force 
generated  by  the  motion  of  this  revolving  satellite. 

The  fourth  step  required  the  philosopher  to  demon- 
strate that  not  only  did  the  planets  gravitate  to  the  sun, 
and  the  satellites  to  their  primaries,  but  that  each  and 
every  one  of  these  bodies,  sun,  planet  and  satellite, 
gravitated  to  the  other,  and  that  each  attracted  the  other 
by  a  force  which  varied  in  the  inverse  ratio  of  the  square 
of  the  distance.  But  here  it  was  found  that  another  mat- 
ter had  to  be  taken  into  account.  The  energy  of  gravi- 
tation did  not  depend  alone  on  distance.  The  power 
exerted  by  the  sun  on  the  planet  Jupiter  was  vastly 
greater  than  that  exerted  by  Saturn,  though  Jupiter 
was  nearly  equidistant  from  these  two  bodies  when  in 
conjunction  with  Saturn.  Newton  proved  that  the 
power  of  gravitation  lodged  in  any  body  depended  on  the 
mass  or  weight  of  the  body,  and  hence  if  the  sun  weighed 


MOTION     AND     GRAVITATION.  183 

x '  *  f 

a  thousand  or  ten  thousand  times  as  much  as  a  planet, 
its  energy  at  equal  distances  would,  by  so  much,  exceed 
that  put  forth  by  the  smaller  orb. 

The  fifth  and  final  step  in  this  sublime,  intellectual 
ascent  to  the  grand  law  of  the  physical  universe,  re- 
quired the  philosopher  to  prove  that  the  force,  power,  or 
energy,  now  called  gravitation,  lodged  in  the  sun,  plan- 
ets and  satellites,  pervaded  equally  every  constituent 
particle  of  each  of  these  bodies,  and  did  not  dwell  alone 
in  the  mathematical  center  of  the  sun  or  planet.  In 
short,  it  was  required  to  show  that  every  ponderable  par- 
ticle of  matter  in  the  whole  universe  possessed  and 
exerted  this  power  of  attraction  in  the  direct  proportion 
of  its  mass,  and  in  the  inverse  ratio  of  the  square  of 
the  distance  at  which  its  energy  was  manifested. 

In  case  these  propositions  could  be  clearly  and  satis- 
factorily demonstrated,  an  instant  and  absolute  revolution 
must  commence  in  the  whole  science  of  astronomy,  and 
the  business  of  future  ages  would  be  nothing  but  the 
verification  of  this  one  grand  controlling  law,  in  its  appli- 
cation to  the  phenomena  presented  in  the  movements  not 
only  of  the  sun's  satellites  and  their  attendants,  but  in 
those  grander  schemes  of  allied  orbs  revealed  by  tele- 
scopic power  in  the  unfathomable  regions  of  the  sideral 
heavens. 

We  shall  now  exhibit  an  outline  of  the  demonstration 
accomplished  by  Newton  to  prove  that  the  law  of  uni- 
versal gravitation,  as  above  announced,  was  the  exact  law 
according  to  which  the  earth  exerted  its  attractive  power 
on  the  moon,  and  held  this  globe  steady  in  its  orbit 

The  intensity  of  any  force,  as  we  have  seen,  is  measured 
by  the  velocity  it  is  capable  of  producing  in  a  heavy 
particle  in  any  unit  of  time,  as  one  swond.  The  earth's 


184 


THE    LAWS    OP 


gravity  at  the  surface  is  measured  then  by  the  space 
through  which  a  body  falls  in  a  second  of  time,  which 
space  (as  experiment  demonstrates)  is  about  sixteen  feet. 
In  case  it  were  possible  to  measure  with  absolute  precision 
the  space  through  which  a  body  falls  at  the  level  of  the 
sea  and  then  at  the  summit  of  a  mountain  (if  there  were 
any  such)  4,000  miles  high,  it  would  be  easy  to  verify 
the  truth  of  the  assumed  law  by  actual  experiment ;  but 
no  mountain  exists  on  the  earth's  surface  whose  height  is 
comparable  with  the  length  of  the  earth's  radius,  and  as 
it  is  absolutely  impossible  to  ascend  vertically  above  the 
earth  to  any  considerable  height,  Newton  soon  saw  that 
no  means  existed  on  the  surface  of  the  earth  whereby 
the  truth  or  falsehood  of  his  assumed  hypothesis  might 
be  ascertained.  In  this  dilemma  he  conceived  the  idea 
that  the  moon  might  be  employed  in  the  experiment,  not 
by  arresting  her  motion  and  dropping  her  literally  to  the 
earth,  but  by  considering  the  earth's  attractive  power  as 
the  cause  of  her  deflection  from  a  rectilineal  movement 
In  one  sense  the  moon  is  perpetually  falling  to  the  earth, 
as  may  be  readily  comprehended  from  an  examination 
of  the  figure  below : — 


MOTION     AND     GRAVITATION.         185 

Let  E  represent  the  earth's  center,  M  a  point  of  the 
moon's  orbit,  in  which  she  is  at  rest  with  no  force  what- 
ever operating  on  her.  Now  let  an  impulse  be  applied  to 
the  moon,  in  the  direction  M  M"',  tangent  to  the  orbit,  or 
perpendicular  to  the  line  M  E,  and  with  such  intensity 
that  at  the  end  of  one  second  of  time  the  moon  will  be 
found  at  M'".  Return  the  moon  to  M,  and  conceiving 
her  to  drop  toward  the  earth,  under  the  power  of  the 
earth's  attraction,  let  us  suppose  that  she  passes  over  the 
distance  M  W  in  one  second.  In  case  the  moon  be  brought 
back  again  to  M,  and  the  impulse  be  now  applied,  and  at 
the  instant  the  moon  darts  off  along  the  straight  line 
MM"',  she  is  seized  by  the  earth's  attractive  power, 
and,  bending  at  once  under  these  conjoined  influences,  she 
commences  her  elliptical  orbit,  and  at  the  end  of  one 
second  is  found  at  M",  passing  over  a  sort  of  curvilinear 
diagonal  of  the  parallelogram  formed  on  the  two  sides 
MM'"  and  MM'.  Now,  it  is  manifest  that  the  line 
M"7  M"  is  equal  to  M  M',  that  is,  that  the  amount  by 
which  the  moon  is  deflected  from  a  right  line  is  precisely 
the  amount  by  which  she  falls  to  the  earth  in  one  second 
of  time.  The  problem  then  resolved  itself  into  a  com- 
putation of  the  line  M  M',  or  the  distance  through  which 
the  moon  ought  to  fall  in  one  second,  in  case  the  assumed 
kw  of  gravition  be  true,  and  the  exact  measurement  in- 
strumentally  of  the  distance  M'"  M",  the  space  through 
which  the  moon  did  fall  in  one  second.  An  exact  equal- 
ity between  these  two  quantities  would  establish  the  law 
of  the  decrease  of  the  earth's  power  of  attraction  to  be  in 
the  inverse  ratio  of  the  square  of  the  distance. 

It  will  be  seen  that  to  compute  how  far  a  body  would 
fall  in  one  second,  when  removed  to  the  moon's  distance, 
in  case  the  earth's  gravity  be  diminished  as  the  square  of 


186  THE     LAWS     OF 

the  distance  increases,  is  a  matter  involving  no  difficulty 
or  uncertainty  whatever,  in  case  we  know  what  the  moon's 
distance  is.  In  like  manner,  to  obtain  the  space  through 
which  the  moon  actually  falls  to  the  earth  in  one  second 
or  minute  of  time,  knowing  her  distance,  admitting  her 
orbit  to  be  circular,  and  assuming  that  we  know  her 
periodic  time,  is  a  problem  of  easy  solution. 

The  chief  difficulty  lay  in  accomplishing  an  accurate 
determination  of  the  moon's  distance  from  the  earth,  a 
matter  which  could  not  be  determined  without  an  accu- 
rate knowledge  of  the  earth's  diameter  or  radius,  as  we 
have  already  seen. 

When  Newton  commenced  his  investigation  the  meas- 
ures which  had  been  executed  of  an  arc  on  the  meridian, 
whereby  the  entire  circumference  of  the  earth  might  be 
obtained  and  its  diameter  computed,  were  comparatively 
imperfect,  yielding  only  an  approximate  value  of  the 
earth's  radius.  As  this  quantity  was  the  unit  employed 
in  the  measure  of  the  moon's  distance,  any  error  in  its 
value  would  be  repeated  some  sixty  times  in  the  value 
of  the  moon's  distance,  and  as  the  gravity  of  the  earth 
was  assumed  to  decrease  as  the  square  of  the  distance  in- 
creased, we  perceive  that  any  error  in  the  radius  of  the 
earth  would  operate  fatally  on  the  solution  of  this  problem, 
involving  the  fate  of  the  most  comprehensive  and  far- 
reaching  hypothesis  ever  conceived  by  the  human  mind. 

Unfortunately  for  Newton,  the  value  of  the  earth's 
diameter,  employed  in  his  first  computations,  was  in 
error,  and  in  executing  the  computation  the  values  of  the 
space  through  which  the  moon  o !  ght  to  fall,  and  the 
space  through  which  she  did  fall,  were  discrepant  by  an 
amount  equal  to  the  sixth  part  of  the  entire  quantity. 
So  great  a  disagreement  was  fatal  to  the  theory  in  the 


MOTION     AND     GRAVITATION.          187 

truth-loving  and  exact  mind  of  Newton,  and  for  many 
years  he  abandoned  all  hope  of  demonstrating  the  truth 
of  his  favorite  hypothesis.  Still  his  mind  was  in  some 
way  powerfully  impressed  with  the  conviction  that  he 
had  divined  the  true  law  of  nature,  and  he  returned  again 
and  again  to  his  computations  in  the  hope  of  removing 
the  discrepancy  by  detecting  some  numerical  error.  It 
was  impossible,  however,  to  find  an  error  where  none  ex- 
isted, and  for  a  time  the  great  philosopher  abandoned  all 
hope  of  accomplishing  this,  the  grandest  of  all  the  efforts 
of  his  own  sublime  genius.  Such  was  the  condition  of 
this  investigation  when  a  new  determination  of  the  value 
of  the  earth's  diameter  was  accomplished  in  France,  by 
the  measurement  of  an  arc  of  the  terrestrial  meridian. 
Having  obtained  this  new  value  of  the  earth's  diameter, 
Newton  resumed  once  more  the  consideration  of  the  pro- 
blem which  had  so  long  occupied  his  thoughts.  The 
new  value  was  substituted  for  the  old — the  moon's  distance 
being  now  accurately  known — the  space  through  which 
a  body  would  fall  in  a  unit  of  time,  under  the  power 
of  gravitation,  when  removed  to  this  new  distance,  was 
rapidly  computed.  In  like  manner  the  distance  through 
which  the  moon  must  actually  fall  was  also  obtained  by 
using  the  new  value  of  the  earth's  diameter. 

It  would  be  impossible  to  form  any  just  idea  of  the  in- 
tense emotions  which  must  have  agitated  the  mind  of  the 
English  philosopher  while  engaged  in  bringing  these  last 
computations  to  a  close.  Upon  a  comparison  of  the  re* 
suits  now  reached  tiere  hung  consequences  of  incalcul- 
able value.  No  less  than  nineteen  years  of  earnest  study, 
of  profound  thought,  and  of  the  most  laborious  investi- 
gation, had  already  been  exhausted  on  this  grand  pro- 
blem, and  now  within  a  few  minutes  the  fate  of  the 


188  THE    LAWS    OF 

theory  and  the  fame  of  the  astronomer  were  to  be  for 
ever  fixed.  No  wonder,  then,  that  we  are  told  that  even 
the  giant  intellect  of  Newton  reeled  and  staggered  under 
the  tremendous  excitement  of  the  moment;  and  seeing 
that  the  figures  were  so  shaping  themselves  as  inevitably 
to  destroy  the  discrepancy  which  had  so  long  existed, 
overcome  by  his  emotions,  Newton  was  compelled  to  ask 
the  assistance  of  a  friend  to  finish  the  numerical  compu- 
tation, and  when  completed  it  was  found  that  the  space 
through  which  the  moon  did  fall  in  a  unit  of  time  was 
identical  with  the  space  through  which  she  ought  to  fall, 
in  case  her  movements  were  controlled  by  a  power  lodged 
in  the  earth's  centre,  and  decreasing  in  energy  as  the 
square  of  the  distance  at  which  it  operated  was  in- 
creased. 

Here  was  presented  the  first  positive  proof  of  the 
prevalence  of  that  universal  law  of  mutual  attraction 
which  energizes  every  particle  of  ponderable  matter  ex- 
isting in  the  universe.  The  earth's  power  of  attraction 
was  thus  shown  to  exert  itself  according  to  a  fixed  law, 
in  deflecting  the  moon  from  the  rectilineal  path  it  would 
otherwise  have  followed,  converting  its  motion  into  one 
of  revolution,  giving  to  its  orbit  the  elliptical  form,  and 
maintaining  at  every  point  of  its  revolution  the  most 
exact  and  perfect  equilibrium. 

It  may,  perhaps,  seem  extraordinary  that  so  much  con- 
sequence should  have  been  attached  by  Newton  to  the 
Buccessful  demonstration  of  this  particular  problem.  If 
he  had  already  shown  that  the  sun's  attraction  upon  the 
planets  followed  the  law  of  the  inverse  ratio  of  the  square 
of  the  distance,  and  that  the  same  law  prevailed  in  the 
attraction  of  the  sun  upon  any  one  planet  at  different 
points  of  its  orbit,  why  regard  as  a  matter  of  such 


MOTION     AND     GRAVITATION.  189 

high  value  the  demonstration  of  the  fact  that  the  earth's 
attraction  upon  the  moon  was  governed  by  the  same 
identical  law.  The  answer,  •  I  think,  may  be  readily 
given. 

The  great  problem  was  this :  Does  one  law  reign  su- 
preme over  all  the  ponderable  masses  of  the  physical 
universe,  or  are  there  many  subordinate  laws  holding  their 
sway  in  the  diverse  systems  and  bodies  which  are  revealed 
by  sight  ?  Might  it  not  be  that  the  sun  would  attract 
the  planets  according  to  one  law,  while  the  planets  might 
attract  their  satellites  according-  to  a  different  law  ?  By 
demonstrating  that  the  earth  controlled  the  moon  by  the 
same  precise  power  whereby  the  sun  controlled  the  plan- 
ets, it  was  demonstrated  that  the  ponderable  matter  of 
the  earth  was  identical  in  character  with  the  ponderable 
matter  of  the  sun,  and  from  this  it  followed  that  as  the 
earth  was  one  of  the  planets  controlled  by  the  power  of 
gravitation  of  the  sun,  so  likewise  the  other  planets 
which  were  controlled  by  the  same  power  must  be  com- 
posed of  ponderable  matter,  governed  by  the  same  laws 
which  reign  in  the  sun  and  earth. 

We  perceive,  then,  that  this  demonstration,  executed 
by  Newton,  in  which  he  proves  that  the  earth's  attrac- 
tion controlled  the  moon,  deserves  the  high  rank  which 
he  has  assigned  it,  for  it  is  nothing  less,  when  conjoined 
with  his  previous  demonstrations,  than  proving  that  every 
globe  which  shines  in  space,  planet  and  satellite,  and 
sun,  are  but  parts  of  one  mighty  system  linked  together 
by  indissoluble  bonds,  forming  one  grand  scheme,  in 
which  each  exerts  its  influence  upon  the  other,  the  whole 
controlled  by  one  supreme  and  all-pervading  law. 

It  only  remained  now  to  extend  by  demonstration  the 
empire  of  the  law  of  universal  gravitation  over  each 


190  THE     LAWS    OF 

particle  of  matter  composing  the  several  worlds.  This 
was  a  problem  of  no  ordinary  difficulty  ;  for  Newton  soon 
discovered  that  in  case  a  mass  of  ponderable  matter  were 
fashioned  into  the  shape  of  a  sphere,  that  for  all  the 
purposes  of  computation  it  would  be  safe  to  consider  the 
entire  globe  as  concentrated  in  one  single  point  at  the 
centre.  Observation  taught  that  all  the  planets,  as  well 
as  their  satellites,  were  bodies  of  globular  form,  and  hence 
in  applying  the  law  of  universal  gravitation  to  the  study 
and  computation  of  their  movements,  the  same  results 
would  be  obtained  by  admitting  the  whole  force  of  attrac- 
tion belonging  to  these  bodies  to  be  concentrated  in  their 
central  points,  or  to  be  distributed  among  the  different 
particles  composing  the  globe.  To  show,  then,  that 
gravity  resided  in  every  particle  composing  a  globe,  and 
not  in  its  central  point,  was  an  impossible  thing,  so  far 
as  the  distant  worlds  were  concerned.  In  the  world  which 
we  inhabit,  however,  and  where  we  can  study  its  indi- 
vidual portions,  and  where  we  can  penetrate  to  certain 
depths  toward  its  center,  it  may  not  be  impossible  to 
learn  whether  the  power  of  gravitation  dwells  in  every 
ponderable  atom  which  goes  to  make  up  the  entire 
earth,  or  whether  it  is  concentrated  in  the  central  point 
alone. 

There  are  several  methods  which  may  be  employed  to 
ascertain  whether  .there  be  any  power  of  attraction  in 
separate  portions  of  the  earth  or  in  the  crust  of  the  earth. 
The  effect  of  a  high  mountain  on  the  direction  of  the 
plumb-line,  (which  at  the  level  of  the  sea  holds  a  direc- 
tion perpendicular  to  the  surface,)  in  causing  it  to  devi- 
ate from  this  direction,  may  be  measured  with  suffi- 
cient accuracy  to  demonstrate  the  power  of  attraction 
existing  in  the  mountain.  Such  an  experiment,  however, 


MOTION     AND     GRAVITATION.         191 

could  not  be  employed  to  demonstrate  that  the  law  of 
universal  gravitation  prevailed  among  the  particles  com- 
posing the  mountain,  it  would  only  show  that  there  was 
a  power  of  attraction  exerted  by  the  mountain,  and  in 
case  we  knew  the  exact  amount  of  deviation  of  the  plumb- 
line  from  the  vertical,  and  the  magnitude  of  the  moun- 
tain, as  well  as  the  law  according  to  which  its  attractive 
power  was  exerted,  we  could  then  obtain  the  quantity  of 
matter  contained  in  the  mountain  mass. 

A  second  method  may  be  employed  to  ascertain 
whether  the  whole  power  of  gravitation  is  lodged  in  the 
center  of  the  earth  or  is  distributed  among  all  its  constit- 
uent particles.  If  it  were  possible  to  penetrate  toward 
the  earth's  center,  a  thousand  miles  below  the  surface, 
and  there  drop  a  heavy  body,  and  measure  the  space 
through  which  it  falls  in  a  unit  of  time,  if  this  measured 
space  should  be  identical  with  that  over  which  the  body 
ought  to  fall,  on  the  supposition  that  its  velocity  de- 
pended simply  on  its  distance  from  the  center,  such  an 
experiment  would  demonstrate  that  the  earth's  gravitat- 
ing force  resided  in  the  central  point  alone ;  this  experi- 
ment cannot  be  performed  in  the  exact  manner  announced, 
but  it  can  be,  and  has  been  substantially  performed,  with 
very  great  delicacy,  in  the  following  manner :  ' 

It  is  found  that  a  pendulum  of  given  length  will  vibrate 
seconds  at  the  equator  of  the  earth. .  If  this  pendulum 
be  removed  nearer  to  the  earth's  center  by  carrying  it 
toward  the  poles,  the  power  of  gravitation  producing  its 
vibration  thereby  growing  more  intense,  the  pendulum 
will  vibrate  more  than  sixty  times  in  a  minute,  and  thus 
the  number  of  vibrations  in  a  given  time  becomes  a  very 
exact  means  of  measuring  the  distance  of  any  point  on 
the  earth's  surface  from  its  center.  These  experiments, 


192  THE     LAWS     OF 

however,  are  performed  upon  the  earth's  surface.  If,  in- 
stead of  removing  the  pendulum  from  the  equator  toward 
the  poles,  and  thereby  reducing  its  distance  from  the 
earth's  center,  this  distance  were  reduced  by  the  same 
amount  by  transporting  the  pendulum  vertically  down- 
ward into  a  deep  mine — if  distance  alone  from  the  center 
be  the  cause  affecting  the  time  of  the  vibration  of  the 
pendulum — then  the  number  of  vibrations  in  a  unit  of 
time  will  be  the  same  in  the  mine  as  at  a  point  on  the  ex- 
terior equidistant  from  the  earth's  center.  When  this 
experiment  comes  to  be  performed  it  is  found  that  there 
is  a  great  difference  between  the  number  of  vibrations  in 
the  interior,  when  compared  with  the  number  of  vibra- 
tions at  the  exterior,  at  equal  distances  from  the  center, 
in  any  unit  of  time,  say  a  mean  solar  day,  clearly  de- 
monstrating that  the  matter  of  the  earth,  lying  above  the 
pendulum  located  in  the  mine,  produces  a  very  sensible 
and  powerfal  effect  upon  the  number  of  its  vibrations. 

Here,  af.ain,  we  find  it  impossible,  from  this  experi- 
ment, to  determine  the  exact  law  which  regulates  the  at- 
tractive pc'yer  of  the  individual  particles  composing  the 
earth,  but  we  do  demonstrate  the  fact  that  the  earth's 
gravity  if  lot  concentrated  at  its  center,  but  dwells,  ac- 
cording t  some  law,  in  all  the  atoms  which  compose  its 
mass;  ?;>d  this  law,  we  shall  prove  hereafter,  is  none 
other  t/,an  the  great  law  of  universal  gravitation. 

It  is  impossible  to  form  a  just  idea  of  the  vast  import- 
ance which  attaches  to  the  grand  discovery  of  Newton. 
It  worked  out,  instantly  and  absolutely,  a  complete  rev- 
olution in  the  whole  science  of  astronomy.  Previous  to 
the  discovery  of  the  law  of  universal  gravitation  all  the 
observations  upon  the  stars  and  planets,  which  liad  been 
accumulating  for  so  many  centuries,  could  only  be  re- 


MOTION     AND     GEAVITATION.         193 

s 

garded  as  so  many  isolated  facts,  having  no  specific  re- 
lation the  one  to  the  other.  The  planets  were  indepen- 
dent orbs,  moving  through  space  in  orbits  peculiar  to 
themselves,  and  only  united  by  the  single  fact  that  the 
sun  constituted  the  common  center  of  revolution.  The 
discovery  made  by  Newton  converted  this  scheme  of  iso- 
lated worlds  into  a  grand  mechanical  system,  wherein 
each  orb  was  dependent  upon  every  other,  each  satellite 
affecting  every  other,  and  the  whole  complex  scheme 
gravitating  to  the  common  center,  which  exerted  a  pre- 
dominant power  over  each  and  every  one  of  these  revolv- 
ing worlds. 

Those  eccentric  bodies  which  we  denominate  cowete, 
whose  abrupt  appearance  in  the  heavens  with  their  glow- 
ing trains  of  light,  whose  rapid  movements  and  sudden 
disappearance  have  excited  such  a  deep  interest  in  all 
ages  of  the  world,  were  found  not  to  be  exempt,  as  we 
shall  hereafter  show,  from  the  empire  of  gravitation. 


CHAPTER    X. 

THE  LAWS  OF  MOTION  AND    GRAVITATION    APPLIED   TO 
A  SYSTEM   OF  THREE   REVOLVING  BODIES. 


A  SYSTEM  OF  'TWO  BODIES.— QUANTITIES  REQUIRED  IN  ITS  INVESTIGATION.— 
FIVE  IN  NUMBER.— SUN  AND  EAHTH.— SUN,  EARTH  AND  MOON,  AS  SYSTEMS 
OP  THREE  BODIES.— THR  S0N  SUPPOSED  STATIONARY — CHANGED  FIGURE  OF 
THE  MOON'S  ORBIT. — SUN  REVOLVING  (  'HANGES  THE  POSITION  OF  THE  MOON'S 
ORBIT. — SOLAR  ORBIT  ELLIPTICAL. — EFFECTS  RESULTING  FROM  THE  INCLINA- 
TION OF  THE  MOON'S  ORBIT. — MOON'S  MOTION  ABOVE  AND  BELOW  THE  PLANK 
OF  THE  ECLIPTIC. — REVOLUTION  OF  THE  LINE  OF  NODES, — SUN,  EARTH  AND 
PLANET,  AS  THE  THREE  BODIES.— PERTURBATIONS  DESTROY  THE  RIGOR  OF 
KEPLER'S  LAWS.— COMPLEXITY  THUS  INTRODUCED.— INFINITESIMAL  ANALY- 

-DlFFERENCE  BETWEEN   GEOMETRICAL  AND  ANALYTICAL  REASONING. 


WE  shall  now  present,  as  clearly  as  we  can,  with- 
out the  aid  of  mathematical  reasoning,  the  application 
of  the  laws  of  motion  and  gravitation  to  the  circum- 
stances arising  in  a  system  of  three  hodies  mutually 
affecting  each  other.  We  will  commence  even  with  a 
simpler  case,  and  suppose  a  solitary  planet  to  exist,  ^sub- 
jected to  the  attractive  power -of  one  sun,  and  that  these 
are  the  only  bodies  in  the  universe.  Let  us  consider 
what  quantities  are  demanded  to  render  it  possible  for 
the  mathematician  to  take  account  of  the  circumstances 
of  motion  which  will  belong  to  this  solitary  world. 

First  of  all,  it  is  evident  that  the  quantity  of  matter 
contained  in  the  sun,  or  its  exact  weight,  must  be  known, 
for  the  energy  or  power  of  the  sun  varies  directly  as  its 
mass,  and  two  suns,  so  related  that  the  weight  of  one  is 
tenfold  greater  than  that  of  the  other,  the  heavier  one 


MOTION    AND     GRAVITATION.  195 

will  exert  a  power  of  attraction  tenfold  greater  than  the 
lighter  one. 

In  the  second  place,  we  must  know  the  distance  of  the 
planet  from  the  sun,  for  the  power  of  the  sun's  attrac- 
tion decreases  as  the  square  of  the  distance  at  which  it 
operates  increases ;  so  that  if  at  a  distance  of  unity  it 
exerts  an  attractive  force  which  we  may  call  one,  at  a 
distance  two  this  force  will  be  diminished  to  one-fourth ; 
at  a  distance  three  to  one-ninth ;  at  a  distance  four  to 
one-sixteenth  ;  at  a  distance  ten  to  the  one  hundredth  part 
of  its  first  value. 

In  the  third  place,  the  mass  or  weight  of  the  planet 
must  be  known ;  for  not  only  does  the  sun  attract  its 
planet,  but  in  turn  the  planet  attracts  the  sun,  and  the 
intensity  of  this  attraction,  which  affects  the  motion  of 
the  planet  as  well  as  that  of  the  sun,  depends  exclusively 
upon  the  mass  or  weight  of  the  planet. 

In  the  fourth  place,  we  must  know  the  intensity  of  the 
impulsive  force  which  is  employed  to  start  the  planet 
in  its  orbit,  for  upon  the  intensity  of  this  force  will  the 
initial  velocity  of  the  planet  depend,  and  we  see  readily 
that  the  form  of  the  orbit  as  to  curvature  will  depend 
upon  the  initial  velocity.  The  greater  this  velocity  the 
more  nearly  will  the  curvature  of  the  orbit  coincide  with 
the  straight  line  in  which  the  planet  would  have  moved 
in  case  it  had  been  operated  upon  by  the  impulsive 
force  alone. 

In  the  fifth  place,  before  we  can  completely  master 
the  circumstances  of  motion  to  the  planet,  we  must  know 
the  direction  in  which  the  impulse  is  applied,  for  upon 
this  direction  it  is  manifest  that  the  figure  of  the  orbit 
will  depend.  If  the  impulsive  force  be  applied  in  a  direc- 
tion passing  through  the  sun's  centre,  and  toward  the 


196  THE    LAWS    OF 

sun,  it  is  clear  that  the  planet  will  simply  fall  to  the 
sun  in  a  straight  line.  If  it  met  with  no  resistance  it 
would  pass  through  and  beyond  the  sun's  center  until 
its  velocity  would  be  entirely  overcome  by  the  attraction 
of  gravitation,  when  it  would  stop,  fall  again  to  the  sun, 
and  thus  vibrate  for  ever  in  a  right  line.  In  case  the 
direction  of  the  impulse  is  oblique  to  the  line  joining  the 
planet  and  the  sun,  (the  angle  falling  within  certain 
limits  of  value,)  then  the  planet  will  describe  an  ellip- 
tical figure  in  its  revolution  around  the  sun,  and  will  re- 
turn precisely  to  the  point  of  departure  to  repeat  the  same 
identical  curve,  with  the  same  velocities  precisely  at  each 
of  the  points  of  its  orbit,  in  the  same  exact  order  for 
ever.  In  examining  the  peculiarities  which  distinguish 
the  movements  of  this  revolving  body,  we  shall  find  as  a 
necessary  consequence  of  the  laws  under  which  it  moves 
that  its  motion  must  be  slowest  at  that  point  of  its  orbit 
where  it  is  furthest  from  the  sun.  Leaving  this  point 
as  it  approaches  the  sun,  its  velocity  must  rapidly  in- 
crease; and  will  reach  its  maximum  at  the  perihelion  of 
its  orbit,  where,  being  nearest  to  the  sun,  it  will  move 
with  its  swiftest  velocity.  Receding  now  from  the  center 
of  attraction  it  will  lose  its  velocity  by  the  same  de- 
grees with  which  it  was  augmented,  and  will  again  pass 
its  aphelion  with  its  slowest  velocity.  Thus  we  per- 
ceive that  the  movements  of  a  single  planet  revolving 
about  the  only  sun  in  existence  are  marked  with  great 
simplicity;  and  in  case  the  mathematician  knows  pre- 
cisely the  five  quantities  already  named,  viz :  the  sun's 
mass,  the  planet's  distance,  the  planet's  mass,  the  in- 
tensity of  the  impulsive  force,  and  the  direction  of  this 
force,  it  is  not  at  all  difficult  to  determine  all  the  cir- 
cumstances of  motion  of  the  planet,  and  to  predict  its 


MOTION    AND     GRAVITATION.  197 

place  in  its  orbit  with  absolute  precision  at  the  end  of 
ten  thousand  revolutions. 

We  will  not  at  present  attempt  to  show  how  these  five 
quantities  may  be  obtained.  These  determinations  be- 
long to  the  department  of  instrumental  astronomy,  a 
subject  which  will  be  treated  after  closing  what  we  have 
to  say  on  the  application  of  the  law  of  gravitation  to  the 
movements  of  a  system  of  three  bodies. 

In  case  the  planets  had  been  formed  of  a  material  such 
as  to  be  attracted  by  the  sun,  but  not  to  attract  each 
other,  and  if  the  satellites  had  been  composed  of  a  mate- 
rial such  as  to  be  attracted  by  their  primaries  only,  then 
the  elements  of  the  orbits  of  all  these  revolving  bodies 
would  have  remained  for  ever  absolutely  invariable.  So 
soon,  then,  as  accurate  observation  should  have  furnished 
the  five  quantities  required  in  determining  the  circum- 
stances of  motion  in  any  revolving  body,  mathematical 
computation  would  have  fitted  an  invariable  orbit  to  each 
one  of  these  bodies,  and  would  have  furnished  by  calcu- 
lation the  exact  place  of  each  one  of  these  bodies  in  all 
coming  time.  The  whole  system  would  have  been  one 
of  perfect  equilibrium,  and  although  complexity  would 
have  presented  itself  apparently  in  the  interlacing  revo- 
lutions of  these  revolving  worlds,  yet  absolute  simplicity, 
combined  with  short  periodical  changes,  would  have  re- 
stored each  one  of  these  bodies  to  the  exact  position  occu- 
pied when  first  launched  in  its  orbit. 

This,  however,  is  not  the  case  of  nature.  The  sun 
uot  only  attracts  the  planets,  but  also  attracts  their 
satellites.  The  primary  planets  not  only  attract  their 
satellites,  but  attract  each  other ;  and  thus  not  a  single 
body  exists  in  the  whole  universe  which  is  not  depend- 
ent upon  every  other. 


198  THE    LAWS    OF 

We  have  alieady  seen  that  in  case  the  sun  with  one 
planet  were  the  only  objects  in  existence,  that  having 
traced  the  planet  in  one  single  revolution  round  the  sun, 
the  variations  of  motion  thus  developed  would  be  repeated 
without  the  slightest  change  in  any  succeeding  revolu- 
tion for  all  coming  time. 

Suppose  this  solitary  planet  to  be  the  earth,  and 
that  from  a  knowledge  of  the  weight  of  the  sun,  the  dis- 
tance of  the  earth  from  the  sun,  the  weight  of  the  earth, 
the  intensity  of  the  impulsive  force,  and  the  direction  in 
which  that  force  is  applied  to  start  the  earth  in  its  orbit, 
we  determine  the  elements  of  its  orbit.  The  form  of 
this  orbit,  its  magnitude  and  position  in  space  will  re- 
main absolutely  invariable,  and  the  changes  of  motion 
in  the  first  revolution  will  be  repeated  exactly  in  all 
succeeding  revolutions.  Let  us  now  add  to  our  system 
of  two  bodies  a  third  body,  as  the  moon.  In  case  the 
sun  had  no  existence,  or  was  removed  to  an  infinite  dis- 
tance, then  the  circumstances  of  motion  in  the  moon, 
once  determined,  would  remain  absolutely  invariable,  but 
the  moment  we  unite  the  three  bodies,  the  sun,  earth 
and  moon,  into  a  system  of  three  orbs,  mutually  depend- 
ent upon  each  other,  the  perfection  and  simplicity  which 
marks  a  system  of  two  bodies  is  for  ever  destroyed,  and 
modifications  are  at  once  introduced  into  the  motion  of 
the  earth  revolving  around  the  sun,  and  also  into  that 
of  the  moon  revolving  around  the  earth,  of  an  exceedingly 
complex  and  difiicult  character,  and  requiring  the  high- 
est developments  of  mathematical  analysis  to  grapple  suc- 
cessfully with  this  great  problem,  of  the  three  bodies. 

The  solution  of  this  problem  has  never  been  positively 
accomplished,  but  approximations  of  wonderful  delicacy 
have  been  reached  by  the  successors  of  Newton,  so  that 


MOTION    AND     GRAVITATION.  199 

for  all  practical  purposes  in  astronomy  this  approximate 
solution  may  be  fairly  regarded  as  absolute. 

As  the  plan  laid  down  in  this  work  does  not  admit  the 
use  of  any  but  the  simplest  mathematical  elements,  we 
shall  only  trace  out,  in  general  terms,  the  consequences 
which  must  follow  from  the  introduction  of  a  third  body 
into  a  system  of  two  revolving  orbs,  and,  for  the  purpose 
of  fixing  our  ideas,  we  will  suppose  the  earth  and  moon 
to  be  our  two  bodies.  The  moon's  orbit,  in  magnitude, 
and  figure,  and  position,  is  supposed  to  be  known ;  her 
period  of  revolution  and  the  circumstances  of  her  motion 
in  her  orbit  are  also  supposed  to  be  accurately  determined. 
The  earth  being  fixed  in  position,  and  the  moon  perform- 
ing her  revolution  under  the  laws  of  motion  and  gravita- 
tion, let  us  now  add  to  this  simple  system-  a  third  body, 
the  sun;  and  to  render  our  investigation  as  simple  as 
possible,  we  will  adopt  the  hypothesis  that  the  earth  con- 
tinues at  rest,  but  that  a  new  force,  namely,  the  sun's 
attraction,  now  commences  to  exert  its  influences  upon 
the  moon.  In  order  still  further  to  simplify  the  case, 
let  us  suppose  the  sun's  center  to  be  situated  in  the  pro- 
longation of  the  longer  axis  of  the  moon's  orbit,  and 
that  the  moon,  in  passing  through  her  aphelion,  will 
cross  the  line  joining  the  centers  of  the  earth  and  sun. 
Under  this  configuration  it  is  clearly  manifest  that  the 
figure  of  the  moon's  orbit  will  be  changed,  because  the 
attractive  power  of  the  sun  will  certainly  increase  the 
distance  to  which  the  moon  travels  from  the  earth,  for 
the  velocity  with  which  the  moon  moves  away  from  her 
perihelion  point  will  be  reinforced  by  the  attractive  power 
of  the  sun,  and  thus  her  aphelion  distance  will  be  in- 
creased. By  the  same  reasoning,  it  will  appear  that 
her  perihelion  distance  will  be  somewhat  diminished,  and 


200  THE     LAWS     OF 

thus  the  longer  axis  will  be  increased  in  length,  and  the 
period  of  revolution  of  the  moon  will,  in  like  manner,  be 
increased. 

These  changes  having  been  once  accomplished,  and  the 
moon  having  taken  up  her  new  orbit  under  the  action  of 
the  new  forces,  so  long  as  these  forces  remain  constant, 
that  is,  so  long  as  the  sun  remains  fixed  in  position,  the 
new  orbit  will  remain  as  invariable  as  did  the  old  before 
the  introduction  of  the  sun.  All  the  changes  accom- 
plished by  the  sun's  power,  whereby  the  new  orbit  is 
made  to  differ  from  the  old,  are  called,  in  astronomy, 
perturbations,  and  the  sun  is  called  the  disturbing  body. 

Let  us  now  suppose  the  sun,  retaining  its  distance  from 
the  earth,  to  start  from  its  position  on  the  prolongation  of 
the  longer  axis  of  the  moon's  orbit,  and  to  commence  a 
revolution  around  the*  earth  in  a  circular  orbit,  lying  in 
the  plane  of  the  moon's  orbit.  A  little  reflection  will 
show  us  that  the  moment  the  disturbing  body  commences 
to  move,  the  direction  of  its  attractive  power  upon  the 
revolving  moon  will  begin  to  change  ;  a  new  set  of 
disturbances  will  now  commence,  not  affecting  the  new 
figure  of  the  moon's  orbit,  but  changing  the  position  of  the 
principal  lines  of  the  orbit  in  its  own  plane ;  for  it  is 
clearly  manifest  that  the  strongest  power  will  be  exerted 
to  draw  the  moon  away  from  the  earth  on  the  line  join- 
ing the  centers  of  the  earth  and  sun ;  and  hence  the 
aphelion  point  of  the  moon's  orbit  will  necessarily  try 
to  follow  this  moving  line.  The  subject  will  be  made 
plainer  by  an  examination  of  the  figure  below,  in  which 
E  represents  the  earth  in  the  focus  of  the  moon's 
orbit,  S  the  place  of  the  sun  on  the  prolongation  of 
P  M  the  longer  axis,  P  the  perigee,  and  M  the  apo- 
gee of  the  moon's  orbit.  In  case  the  sun  be  removed 


MOTION     AND    GRAVITATION.          201 

to  S',  and  there  remain  stationary,  it  is  manifest  that 
each  time  the  moon  crosses  the  line  E  S'  it  will  be  sub- 
jected to  the  most  powerful  influence  to  draw  it  away 
from  the  earth  at  E  j  and  in  case  the  sun  remain  station- 


ary for  a  sufficiently  long  time  at  each  of  the  moon's 
revolutions,  the  point  M  will  approach  M',  and  finally  it 
will  actually  fall  on  M',  where  it  will  remain  fixed,  so 
long  as  the  sun  is  stationary. 

In  case,  however,  the  sun  again  advances  in  the  same 
direction,  the  apogee  of  the  moon  will  again  advance,  and 
should  the  sun,  by  successive  steps,  slowly  perform  an 
entire  revolution,  pausing  at  each  step  sufficiently  long  for 
the  moon's  apogee  to  come  up  to  the  line  joining  the 
centers  of  the  earth  and  sun ;  when  the  revolution  of  the 
sun  shall  have  been  completed  the  revolution  of  the 
moon's  apogee  will,  in  like  manner,  have  been  finished. 

If,  instead  of  supposing  the  sun  to  advance  by  successive 
steps,  we  admit  his  uniform  progress,  it  is  clearly  mani- 
fest that  in  each  revolution  of  the  moon,  the  apogee  of  her 
orbit  must  advance  a  certain  amount  in  the  direction  of 
the  sun's  motion,  and,  in  the  end,  a  complete  revolution 
of  the  moon's  apogee  will  be  accomplished  under  the  dis- 
turbing influence  of  the  sun's  attraction. 

9* 


202  THE     LAWS     OF 

We  have  seen  that  if  the  sun  were  stationary  hia 
disturbing  power  would  only  go  to  change  the  figure  of 
the  moon's  orbit,  leaving  the  direction  of  the  longer  axis 
undisturbed.  The  revolution  of  the  sun  in  a  circular 
orbit  by  slow  degrees  accomplishes  an  entire  revolution 
of  the  apogee,  or  of  the  line  of  apsides,  and  thus,  in  case 
the  line  of  apsides  should  perform  its  revolution  in  a 
period  which  shall  be  an  exact  multiple  of  the  period  of 
the  sun's  revolution,  then  at  the  end  of  one  such  cycle 
the  moon  will  have  passed  through  all  the  changes  which 
can  arise  from  the  disturbing  influence  of  the  sun.  These 
changes  will  therefore  be  strictly  periodical,  and  in  the 
end  the  moon  will  return  to  its  first  position,  and  will  re- 
peat the  same  identical  changes  forever. 

We  will  now  consider  the  solar  orbit  to  be  elliptical. 
This  involves,  by  necessity,  a  perpetual  change  in  the 
sun's  distance,  and  as  his  disturbing  power  varies  in  in- 
tensity inversely  with  the  square  of  his  distance,  it  is 
manifest  that  this  variation  in  the  disturbing  force  will 
introduce,  a  corresponding  variation  into  the  figure  of  the 
moon's  orbit.  If  the  sun  be  supposed  to  advance  toward 
the  earth  and  the  moon,  in  the  direction  of  the  line  of 
apsides,  its  disturbing  power  would  be  exerted  to  draw 
the  moon  further  from  the  earth  the  nearer  the  sun  ap- 
proached ;  in  other  language,  to  increase  the  magnitude 
of  the  moon's  orbit  and  the  period  of  her  revolution. 
This  action  will  be  varied  in  case  the  sun  recede  from 
the  earth  along  the  same  line,  and  if  this  approach  and 
recess  were  made  by  successive  steps,  at  intervals  suf- 
ficiently long  to  allow  the  moon's  orbit  to  assume  a  fixed 
form,  then  one  vibration  of  the  sun  advancing  and  re- 
ceding through  equal  space,  would  work  out  a  series  of 
changes  in  the  form  of  the  moon's  orbit  identical  with 


MOTION'AND     GRAVITATION.         203 

those  accomplished  by  each  successive  vibration,  while  in 
all  these  changes  the  direction  of  the  line  of  apsides 
would  remain  fixed. 

If  now  we  suppose  the  advance  and  recess  of  the  sun 
to  be  effected  by  its  revolution  in  an  elliptic  orbit,  then 
we  shall  find  the  changes  of  figure  in  the  moon's  orbit, 
just  noticed,  as  due  to  the  sun's  change  of  distance,  wfl 
be  combined  with  an  advance  and  final  complete  revolu- 
tion of  the  line  of  apsides ;  and  admitting  the  figure  of 
the  sun's  orbit  to  remain  unchanged,  and  the  principal 
axis  of  its  orbit  to  remain  fixed  forever  in  position,  a  time 
will  come  when  the  sun  will  have  been  presented  to  the 
moon  in  every  possible  position,  and  all  the  changes  in 
the  figure  of  the  moon's  orbit,  and  the  revolution  of  the 
line  of  apsides  of  the  moon's  orbit,  due  to  the  revolution 
of  the  sun  in  his  orbit,  will  have  been  accomplished.  The 
moving  bodies  return  to  their  primitive  points  of  depart- 
ure, and  a  new  cycle  of  changes  begins,  to  be  repeated,  in 
the  same  order  forever. 

Thus  far  we^  have  supposed  the  line  of  apsides  of  the 
sun's  orbit  to  remain  fixed  in  position  and  unchanged  in 
length.  It  is  manifest  that  a  revolution  of  the  line  of 
apsides  of  the  sun's  orbit,  definite  in  period  and  fluctua- 
tions in  its  length  also  periodical,  would  introduce  addi- 
tional fluctuations  in  the  moon's  motion,  and  in  the 
length  and  position  of  the  principal  axis  of  her  orbil. 
But  while  we  rise  in  complexity,  and  while  the  periods 
requisite  for  effecting  all  these  changes  expand  into  ages, 
we  still  recognize  the  great  fact  that  periodicity  re- 
mains, and  that  in  the  end,  at  the  termination  of  a  vast 
cycle,  the  revolving  bodies  must  return  again  to  their 
points  of  departure  to  repeat  the  same  identical  changes 
through  endless  ages. 


204  THE     LAWS     OF 

In  all  our  reasoning  thus  far  we  have  supposed  that 
the  three  bodies  under  consideration  always  lie  in  the 
same  plane ;  in  other  language,  that  the  planes  of  the 
orbits  of  the  moon  and  earth  coincide.  This,  however, 
is  not  the  case  of  nature.  As  we  have  already  seen,  the 
moon's  orbit  is  inclined  to  the  plane  of  the  ecliptic  under 
an  angle  of  about  5° — the  line  of  intersection  of  the 
two  planes  being  called  the  line  of  the  moon's  nodes, 
which  line  must,  of  course,  always  pass  through  the  earth's 
center. 

We  shall  now  proceed  to  take  this  inclination  into 
consideration,  and  ascertain  whether  the  sun's  disturbing 
force  has  any,  .and  if  any,  what  effect  on  the  position  of 
the  line  of  nodes,  and  on  the  inclination  of  the  moon's 
orbit.  For  this  purpose  let  us  suppose  the  earth  to  be 
stationary,  and  that  the  line  of  nodes  of  the  moon's  orbit 
holds  a  position  perpendicular  to  the  line  joining  the 
centers  of  the  earth  and  sun,  and  that  the  moon  starts 
from  her  ascending  node  to  describe  that  portion  of  her 
orbit  lying  above  the  plane  of  the  ecliptic.  The  power 
of  attraction  of  the  sun  will  manifestly  exert  itself  in 
such  manner  as  to  cause  the  moon  to  deviate  from  its 
old  orbit  and  to  describe  a  new  orbit,  which  will  lie  in 
all  its  points  a  little  nearer  to  the  plane  of  the  ecliptic. 
The  moon  will  not,  therefore,  rise  in  this  superior  part 
of  her  orbit  as  high  above  the  plane  of  the  ecliptic  as  she 
did  before  her  motion  was  disturbed  by  the  sun ;  and  in 
descending  to  pass  through  her  node  she  will  clearly  reach 
the  plane  of  the  ecliptic  quicker  than  she  did  when  un- 
disturbed, and  pass  through  her  node  at  a  point  nearer 
to  herself  than  that  occupied  by  the  former  node :  in 
other  language,  the  old  node  comes  up  to  meet  the  ad- 
vancing moon,  and  thus  takes  up  a  retrograde  motion. 


MOTION     AND     GRAVITATION.         205 

Let  us  now  examine  the  motion  of  the  moon  in  that 
portion  of  her  orbit  lying  beneath  the  plane  of  the  eclip- 
tic and  most  remote  from  the  sun.  Here  the  sun's  dis- 
turbing influence  will  be  diminished  somewhat,  in  conse- 
quence of  the  increased  distance  at  which  it  operates,  but 
its  effect  will  manifestly  be  to  cause  the  moon  to  descend 
more  rapidly  and  to  reach  a  lower  point  beneath  the 
ecliptic  than  when  undisturbed,  increasing  the  inclination 
of  the  plane  of  the  orbit,  and  causing  the  moon  to  reach 
her  ascending  node  at  a  point  earlier  than  when  undis- 
turbed, and  thus  producing  a  retrocession  or  retrograde 
motion  of  the  line  of  nodes.  Thus  it  appears  that  in  the 
long  run  the  sun's  disturbing  influence  will  tend  to 
change  within  certain  limits  the  angle  of  inclination  of 
the  moon's  orbit ;  and,  indeed,  if  the  earth  were  fixed  in 
position,  would  finally  destroy  this  inclination  entirely, 
reducing  the  plane  of  the  moon's  orbit  to  absolute  coinci- 
dence with  that  of  the  earth  ;  but  as  the  moon  is  carried 
by  the  earth  around  the  sun,  and  as  the  moon's  orbit  in 
the  course  of  an  entire  revolution  of  the  earth  is  thus 
presented  to  the  sun  at  opposite  points  of  the  orbit  under 
reverse  circumstances,  there  is  a  compensation  accom- 
plished, so  far  as  the  angle  of  inclination  is  concerned,  and 
also  a  partial  compensation  in  the  retrogression  of  the 
line  of  nodes  of  the  moon's  orbit,  but  not  such  as  to  pre- 
vent, in  the  end,  a  complete  revolution  of  the  moon's 
nodes  in  a  period  which  we  have  already  seen  amounts  to 
eighteen  years  and  two  hundred  and  nineteen  days. 

We  have  thus  attempted  to  present  a  general  account 
of  the  effect  of  a  disturbing  force.  These  same  principles 
may  be  extended  yet  further,  and  will  give  a  general 
idea  of  the  effects  produced  by  the  planets  and  their 
satellites  upon  each  other. 


J06  THE    LAWS     OF 

If  we  return  for  a  moment  to  the  hypothesis  that  the 
-iartli  is  the  only  planet  revolving  about  the  sun,  the  mag- 
nitude of  its  orbit,  as  well  as  the  length  and  position  of  the 
line  of  apsides,  will  remain  for  ever  fixed.  If,  however,  we 
introduce  into  our  system  a  new  planet  revolving  in  an 
orbit  interior  to  that  of  the  earth,  whatever  force  is  exerted 
upon  the  earth  by  the  attractive  power  of  this  new  planet 
will  go  to  reinforce  the  power  exerted  by  the  sun ;  and 
hence  the  disturbing  influence  of  the  planet  will  tend  to 
diminish  the  magnitude  of  the  earth's  orbit,  and  to  de- 
crease its  periodic  time.  If  the  disturbing  planet  revolve  in 
the  same  direction  with  the  earth,  by  applying  the  reason- 
ing hitherto  used  we  shall  find  that  its  effect  will  be  to  cause 
the  perihelion  point  of  the  earth's  orbit  to  advance  and 
retreat  during  the  revolution  of  the  disturbing  body, 
always  leaving,  however,  a  slight  preponderance  of  the 
advancing  movement  over  the  retrograde. 

In  case  the  disturbing  body  revolve  in  an  orbit  ex- 
terior to  that  of  the  -earth,  then  its  effect  will  be  to  ex- 
pand the  earth's  orbit  and  to  increase  the  periodic  time, 
while  the  influence  exerted  upon  the  position  of  the  line 
of  apsides  will,  in  the  long  run,  produce  an  advance. 

The  reasoning  hitherto  employed  with  reference  to  the 
inclination  of  the  moon's  orbit  to  the  ecliptic  is  directly 
applicable  to  the  effect  produced  by  any  planet  upon  the 
inclination  of  the  orbit  of  any  other  planet,  as  referred 
to  a  fixed  plane.  Take  the  earth  for  example,  and  let 
us  consider  the  effect  of  any  planet  either  interior  or  ex- 
terior upon  the  inclination  of  this  plane  to  any  fixed 
plane.  So  long  as  the  disturbing  body  is  revolving  in 
that  part  of  its  orbit  lying  below  the  plane  of  the  eclip- 
tic the  tendency  of  the  disturbing  force  will  be  to  draw 
the  earth  from  its  undisturbed  path  below  the  plane  of  a 


MOTION    AND     GRAVITATION.  207 

fixed  ecliptic,  while  this  effect  will  be  reversed  whenever 
the  disturbing  planet  shall  pass  through  the  plane  of  the 
ecliptic,  and  commence  the  description  of  that  part  of  its 
orbit  which  lies  above  this  plane. 

From  the  above  reasoning  it  is  clearly  manifest  that  as 
not  a  solitary  planet  or  satellite  is  moving  undisturbed 
under  the  attractive  power  of  its  primary  body,  not  one 
of  the  heavenly  bodies  describes  rigorously  an  elliptic 
orbit,  nor  does  the  line  joining  the  sun  with  any  planet 
sweep  over  precisely  equal  areas  in  equal  times,  neither 
are  the  squares  of  the  periodic  times  of  the  planets  exactly 
proportioned  to  the  cubes  of  their  mean  distances  from  the  i 
sun.  In  short,  every  law  of  Kepler,  whereby  perfect 
harmony  seemed  to  be  introduced  among  the  heavenly 
bodies,  is  now  seen  to  fail  in  consequence  of  the  law  of 
universal  gravitation,  and  we  find  ourselves  surrounded 
by  a  problem  of  wonderful  grandeur,  but  of  almost  in- 
finite complexity.  Before  this  problem  can  be  fully 
solved  we  must  measure  the  distance  which  separates 
every  planet  from  the  sun,  and  which  divides  every  satel- 
lite from  its  primary ;  we  must  weigh  the  sun  and  all  his 
planets  and  every  satellite  ;  we  must  determine  the  exact 
periods  of  revolution  of  each  of  these  revolving  worlds ; 
and  when  all  this  is  accomplished,  to  trace  out  the  re- 
ciprocal influences  of  each  upon  the  other  demands 
powers  of  reasoning  far  transcending  the  abilities  of  the 
most  powerful  genius,  and  hence  the  mind  must  either 
forego  the  resolution  of  this  problem,  or  prepare  for  itself 
some  mental  machinery  which  shall  give  to  thought  and 
reason  the  same  mechanical  advantages  which  are  ob- 
tained for  the  physical  powers  of  the  body  by  the  in- 
vention and  construction  of  the  mighty  engines  of  modern 
mechanics. 


208  THE     LAWS     OF 

This  has  actually  been  accomplished  in  the  discovery 
and  gradual  perfection  of  a  branch  of  mathematics  called 
the  infinitesimal  analysis.  Up  to  the  time  of  Newton, 
the  mind  employed  alone  the  reasoning  of  geometry  in 
the  examination  and  discussion  of  the  problems  presented 
in  the  heavens.  Even  Newton  himself  was  content  to 
publish  to  the  world  the  results  of  the  application  of  the 
law  of  gravitation  to  the  movement  of  the  planets  and 
their  satellites  under  a  geometrical  form,  exhibiting,  in 
the  use  of  these  old  methods,  a  sort  of  gigantic  power 
which  has  ever  remained  as  a  monument  of  his  wonder- 
ful ability. 

He  was,  however,  fully  conscious  of  the  fact,  that  the 
mind  demanded  for  its  use,  in  a  full  investigation  of  the 
physical  universe — in  the  pursuit  of  these  flying  worlds, 
journeying  through  space  amid  such  a  crowd  of  disturb- 
ing influences — a  far  more  subtle,  pliable,  and  powerful 
mental  machinery  than  that  furnished  in  the  cumbrous 
forms  of  geometrical  reasoning.  Conscious  of  this  want, 
the  genius  of  Newton  supplied  the  deficiency,  and  gave 
to  the  world  the  infinitesimal  analysis,  which,  as  im- 
proved and  extended  by  the  successors  of  the  great  En- 
glish philosopher,  has  enabled  man  to  accomplish  results 
which  seem  to  place  him  almost  among  the  gods. 

The  plan  of  our  work  does  not  permit  any  attempt  to 
explain  the  nature  and  powers  of  this  new  method  of 
reasoning.  We  can  only  illustrate  imperfectly  the  differ- 
ence between  the  use  of  geometry  and  analysis.  The 
demonstration  of  a  problem  by  geometry  demands  that 
the  mind  shall  comprehend  and  hold  the  first  step  in  the 
train  of  reasoning,  then,  while  the  first  is  held,  the  second 
must  be  comprehended,  and  while  intently  holding  these 
two  steps,  the  third  must  be  mastered  and  held,  while 


MOTION     AND     GRAVITATION.         209 

the  mind  advances  to  the  fourth  step ;  thus  progressing 
with  a  constantly  accumulating  weight  oppressing  the  at- 
tention, and  tending  to  crush  and  destroy  further  effort 
to  advance,  till,  finally,  the  steps  become  so  numerous 
and  complex  that  only  those  possessed  of  a  genius  of  sur- 
passing vigor  are  able  to  reach  in  safety  the  last  step, 
and  thus  grasp  the  full  demonstration  of  the  problem. 
Such  is  the  reasoning  of  geometry.  That  of  analysis  is 
entirely  different.  Here  the  great  effort  is  put  forth  to 
master  fully  and  perfectly  the  conditions  of  the  problem, 
and  then  to  fasten  upon  the  problem  thus  mastered  the  an- 
alytical machinery  demanded  in  its  resolution.  This  once 
accomplished,  the  mind  puts  forth  its  energy  and  accom- 
plishes the  first  step,  and  may  there  stop  and  rest,  in  the 
full  confidence  that  what  has  been  gained  can  never  be 
lost.  Days,  even  months  may  pass,  before  the  problem 
be  resumed,  but  in  this  lapse  of  time  there  is  no  loss,  and 
the  investigation  may  be  taken  up  precisely  where  it  was 
left  off;  and  so  one  step  after  another  may  be  taken, 
each  dependent  on  the  other,  but  each  in  some  sense 
stereotyped  as  the  mind  advances,  and  remaining  fixed 
without  the  putting  forth  of  any  mental  effort  to  retain 
it.  In  short,  geometry  demands  a  vigor  of  mind  suffici- 
ent to  grasp,  and  hold  at  the  same  instant,  every  link  in 
the  longest  and  most  complex  chain  of  reasoning,  while 
analysis  only  requires  a  power  of  genius  sufficient  to  deal 
with  individual  links  in  succession;  thus,  in  the  end, 
reaching  the  conclusion  by  short  and  comparatively  easy 
mental  marches. 


CHAPTER    XI. 


INSTRUMENTAL    ASTRONOMY. 

METHOD  FOR  OBTAINING  THE  MASS  OP  THE  Sim.— FOB  GETTTNG  THE  MASS  o»  A 
PLANET  WITH  A  SATELLITE. — FOB  WEIGHING  A  PLANET  HAVING  NO  SATEL- 
LITE.—FOB  WEIGHING  THE  SATELLITES.— PLANETARY  DISTANCES  To  B» 
MEASURED.— INTERVALS  BETWEEN  PRIMARIES  AND  THEIB  SATELLITES  TO  BK 
OBTAINED. — INTENSITY  AND  DIRECTION  OF  THE  IMPULSIVE  FORCES  TO  BE 
DETERMINED. — THKSK  PROBLEMS  ALL  DEMAND  INSTRUMENTAL  MEASURES. — 
DIFFERENTIAL  PLACES. — ABSOLUTE  PLACES. — THE  TRANSIT  INSTRUMENT.— 
ADJUSTMENTS. — INSTRUMENTAL  ERRORS. — CORRECTIONS  DUE  TO  VARIOUS 
CAUSES. — AMERICAN  METHOD  OF  TRANSITS. — MERIDIAN  CIRCLE. — THE  DE- 
CLINOMETER. 

THE  general  reasoning  presented  in  the  preceding 
chapter  can  only  be  reduced  to  exact  application  after 
having  obtained  the  numerical  values  of  the  quantities 
demanded  in  the  investigation.  The  mathematician  may 
assume  these  quantities  at  his  pleasure,  and  with  the  as- 
sumed weight  of  his  sun,  and  planets  and  satellites,  and 
with  their  assumed  distances,  and  with  the  assumed  di- 
rections and  intensities  of  the  impulsive  forces,  he  may 
master,  by  analytical  reasoning,  all  the  circumstances 
attending  the  revolution  of  these  supposed  worlds,  and 
thus  trace  their  imaginary  history  for  ages,  either  past  or 
future. 

This  is  the  work  of  the  pure  mathematician.  The 
physical  astronomer  takes  up  the  general  mathematical 
reasoning  thus  perfected,  and  to  employ  it  in  writing  out 


INSTRUMENTAL    ASTRONOMY.  211 

the  history  of  the  real  bodies  constituting  the  solar  sys- 
tem, he  must  measure  the  actual  distances  between  the 
sun  and  the  planets,  and  the  distances  from  each  primary 
to  its  satellites ;  he  must  weigh  exactly  the  sun  and  each 
of  the  planets  and  satellites,  and  he  must  measure  in 
some  way  the  direction  and  intensity  of  the  impulsive 
forces  by  which  the  planets  and  their  satellites  were  pro- 
jected m  their  respective  orbits. 

We  shall  now  proceed  to  show  that  the  determination 
of  all  these  quantities  depends  on  exact  astronomical 
measurements,  which  measurements  demand  the  inven- 
tion and  construction  of  instruments  of  the  highest  order 
of  power,  delicacy  and  perfection. 

To  WEIGH  THE  SUN  AND  PLANETS. — Let  it  be  borne  in 
mind  that  the  law  of  gravitation  asserts  that  bodies  at- 
tract with  a  force  or  power  directly  in  proportion  to  their 
mass  or  weight.  Hence  a  sun,  weighing  twice  as  much 
as  the  central  orb  of  the  solar  system,  would  (at  the 
same  distance)  attract  with  a  double  force.  The  same  is 
true  of  the  earth ;  and  if  it  were  possible  to  hollow  out 
the  interior  of  the  earth  until  its  weight  were  reduced  to 
one-half  of  what  it  is  now,  its  power  of  attraction  would 
be  diminished  in  the  same  exact  proportion. 

Thus,  to  know  with  what  power  the  sun  or  any  planet 
or  any  satellite  attracts  a  body  at  a  given  distance,  we  are 
compelled  to  ascertain  the  exact  weight  of  the  sun,  planet, 
or  satellite. 

"We  shall  show  hereafter  that  it  is  possible  to  reach  an 
approximate  value  of  the  weight  of  the  earth  in  pounds 
avoirdupois,  but  for  our  present  purpose  it  will  be  sufficient 
to  state  that  the  weight  of  the  earth  is  well  represented 
by  the  intensity  of  its  power  of  attraction  at  a  unit's  dis- 
tance from  its  center.  For  this  unit  of  length  we  will 


212  INSTRUMENTAL    ASTRONOMY. 

take  the  earth's  radius,  and  hence  a  body  on  the  surface 
is  attracted  by  a  force  or  power  such  as  will  measure  the 
mass  or  weight  of  the  earth ;  but  the  intensity  of  any 
force  is  measured  by  the  quantity  of  motion  it  is  capable 
of  generating  in  a  given  time.  Hence  the  intensity 
of  the  earth's  attractive  power  will  be  correctly  meas- 
ured by  the  velocity  it  impresses  on  a  body  free  to 
fall,  in,  say,  one  second  of  time.  This  is  a  matter  of  the 
simplest  experiment,  by  which  it  is  found  that  the  earth's 
attractive  power  generates  in  one  second  a  motion  in  a 
falling  body  such  as  to  carry  it  over  a  space  equal  to 
about  sixteen  feet  in  one  second.  In  case  the  earth  were 
twice  as  heavy,  the  space  passed  over  by  a  falling  body  in 
one  second  would  be  doubled,  and  so  forward  in  like  pro- 
portion for  any  increase  of  weight. 

Having  thus  found  a  measure  of  the  weight  of  the  earth 
in  the  space  passed  over  in  a  second  of  time  by  a  falling 
body,  in  case  it  were  possible  to  transport  this  body  to 
the  surface  of  the  planet  Venus  (assuming  the  diameter 
of  Venus  and  the  earth  to  be  equal),  then  permitting  it  to 
fall,  and  measuring  the  space  over  which  it  passes  in  one 
second,  this  space  would  hold  the  same  proportion  to  six- 
teen feet  as  the  weight  of  Venus  does  to  that  of  the  earth. 
If  the  diameters  of  the  planets  are  unequal,  then  we 
must  take  into  account  the  fact  that  the  falling  body  is 
not  at  equal  distances  from  the  centers  of  the  planets, 
and  that  the  force  of  attraction  is  thus  diminished  in- 
versely as  the  square  of  the  distance  from  the  center  is 
increased.  Let  us  attempt  to  weigh  two  planets  whose 
diameters  are  in  the  proportion  of  one  to  two.  At  the  sur- 
face of  the  smaller  planet  suppose  the  body  falls  sixteen  feet 
in  one  second,  while  at  the  surface  of  the  larger  planet  it 
passes  over  sixty-four  feet  in  the  same  time.  In  case  the 


INSTRUMENTAL    ASTRONOMY.  213 

diameters  were  equal  this  result  would  show  that  one 
body  was  four  times  as  heavy  as  the  other  ;  but  the  fall- 
ing body  is  twice  as  far  from  the  center  of  the  large 
planet  as  it  is  from  the  center  of  the  small  one,  and  hence 
the  force  or  power  of  attraction  of  the  large  planet  is 
only  one-fourth  part  what  it  would  have  been  in  case  the 
falling  body  had  been  brought  to  within  one  unit  of  its 
center.  If,  then,  with  an  energy  reduced  at  a  distance 
of  two  units  to  one  quarter,  it  causes  a  fall  of  sixty-four 
feet  in  one  second,  the  entire  energy  would,  at  a  unit's 
distance,  cause  a  fall  through  four  times  sixty-four  feet, 
or  through  256  feet,  and  hence  the  weights  of  the  plan- 
ets under  examination  are  in  the  proportion  of  16  to 
256  or  1  to  16. 

The  train  of  reasoning  here  presented  may  be  extended 
to  embrace  any  given  case,  and  if  it  were  possible  to 
make  the  experiment  of  the  falling  body,  as  above  de- 
scribed, at  the  surfaces  of  the  sun,  planets  and  satellites, 
(admitting  that  we  know  the  diameters  of  all  these  bodies,) 
then  would  it  be  possible  to  ascertain  their  masses,  as 
compared  with  that  of  the  earth,  taken  as  a  unit. 

But  it  is  impossible  to  pass  to  the  sun  and  planets  for 
such  experimentation,  and  hence  we  must  devise  some 
substitute  which  may  fall  within  the  limits  of  practicabil- 
ity. To  obtain  the  relative  weights  of  the  sun  and  earth 
we  have  only  to  call  to  mind  the  fact  that  the  moon,  un- 
der the  power  of  the  earth's  attraction,  is  ever  falling 
away  from  the  rectilineal  path  in  which  it  would  fly 
but  for  this  very  power  of  attraction,  while  in  like 
manner  the  earth  is  ever  falling  away  from  the  right 
line  in  which  it  would  move  but  for  the  attractive 
energy  of  the  sun.  Here,  then,  are  two  bodies,  the 
earth  falling  to  the  sun,  the  moon  falling  to  the  earth ; 


214        INSTRUMENTAL     ASTEONOMT. 

and  in  case  we  could  measure  the  precise  distance  which 
each  of  these  bodies  falls,  under  the  respective  powers  of 
attraction  exerted  on  them,  taking  into  account  the  effect 
produced  on  the  two  forces  by  the  inequality  of  the  dis- 
tances at  which  they  operate,  we  should  reach  the  exact 
relative  weights  of  the  sun  and  earth.  Thus,  admitting 
that  the  distance  at  which  the  sun  operates  on  the  earth 
is  400  times  greater  than  the  distance  at  which  the  earth 
operates  on  the  moon,  in  case  the  effects  were  equal  the 
sun  would  be  160,000  times  heavier  than  the  earth,  since 
its  power  of  attraction  is  reduced  by  the  distance  in  this 
exact  ratio.  But  again,  admitting  that  we  find,  even 
with  this  high  reduction,  the  sun's  power  on  the  earth  is 
still  two  and  a  half  times  greater  than  the  earth's  power 
on  the  moon,  (as  is  shown  in  their  respective  deflections 
from  a  right  line  in  one  second  of  time,)  then  will  the 
sun  be  2^x160,000  times  heavier  than  the  earth,  and 
this,  indeed,  as  we  shall  find  hereafter,  is  about  the  re- 
lative weights  of  these  two  globes. 

To  resolve  this  great  problem,  then,  of  weighing  the 
sun  against  the  earth,  we  must  first  measure  the  sun's 
distance  and  the  moon's  distance,  and  the  exact  amounts 
by  which  the  earth  and  moon  are  caused  to  fall  away 
from  a  rectilineal  orbit  in  one  second  of  time,  which  meas- 
urements demand  instruments  of  the  highest  order. 

TO  WEIGH  AGAINST  THE  EARTH,  A  PLANET  ATTENDED 

BY  A  SATELLITE. — In  case  any  planet  be  attended  by  a 
satellite,  if  we  can  measure  the  precise  distance  separat- 
ing these  two  bodies,  and  determine  the  period  of  revolu- 
tion of  the  satellite,  we  can  thence  derive  the  weight  of 
the  planet  as  compared  with  that  of  the  earth.  To  fix 
our  ideas,  let  us  suppose  Jupiter's  nearest  satellite  to  bo 
as  far  from  Jupiter  as  our  moon  is  from  the  earth,  and  to 


INSTRUMENTAL     ASTRONOMY.          215 

perform  its  orbital  revolution  in  the  same  exact  time  oc- 
cupied by  the  moon.  This  would  prove  Jupiter  to  be 
just  as  heavy  as  the  earth.  But  suppose  now  that  at 
equal  distances  Jupiter's  moon  revolves  ten  times  as 
rapidly  as  the  earth's  moon,  this  fact  proves  that  Jupiter 
must  be  one  hundered  times  as  heavy  as  the  earth.  This 
is  evident  from  what  we  have  already  said,  that  the 
centrifugal  force  in  any  revolving  body  increases  as  the 
square  of  the  velocity ;  and  as  the  moon  of  Jupiter  is 
now  supposed  to  revolve  ten  times  as  fast  as  our  moon 
its  centrifugal  force  will  be  one  hundred  times  as  great 
as  that  of  the  earth's  moon ;  and  hence  Jupiter's  attrac- 
tion to  counterbalance  this  tendency  to  fly  from  the  cen- 
ter must  be  one  hundred  fold  greater  than  that  of  the 
earth.  This  is  on  the  hypothesis  of  equal  distances. 
But  if  Jupiter's  moon  be  supposed  to  be  twice  as  remote  ' 
from  its  primary,  and  to  revolve  ten  times  as  rapid  as 
our  moon,  then  will  it  be  demonstrated  that  Jupiter  is 
one  hundred  times  heavier,  on  account  of  the  square  of 
the  velocity  of  the  revolving  moon,  but  this  weight  must 
be  multiplied  by  the  square  of  two  on  account  of  the 
double  distance  at  which  it  acts.  Hence,  under  these 
circumstances  Jupiter  would  be  400  times  as  heavy  as 
the  earth. 

Thus,  to  determine  the  weight  of  a  planet  in  terms  of 
the  earth's  weight  as  unity,  we  must  learn  the  exact  dis- 
tance and  periodic  time  of  our  moon,  and  also  the  interval 
by  which  the  planet  and  its  moon  are  separated,  as  well 
as  the  period  of  revolution  of  the  satellite,  all  of  which 
again  demand  the  use  of  instruments  of  a  high  order  of 
accuracy  and  delicacy. 

TO  WEIGH  A  PLANET   HAVING  NO    SATELLITE. — Three 

of  the  planets,    viz.  :  Mercury,  Venus,    and   Mars,   so 


216          INSTRUMENTAL     ASTRONOMY. 

far  as  known,  are  not  accompanied  by  a  moon.  The 
preceding  method  of  obtaining  the  mass  or  weight  will 
not  apply  to  either  of  these  planets.  It  is  only  after 
acquiring  a  very  exact  knowledge  of  the  movements  of 
the  planets  whose  masses  may  be  derived  from  their  satel- 
lites that  it  becomes  possible  to  determine  the  weights  of 
the  remaining  planets.  Let  us  suppose  that  the  earth 
alone  revolved  around  the  sun,  and  that  its  orbit  was 
perfectly  determined.  In  an  exterior  orbit  of  known 
dimensions  let  us  place  the  planet  Mars.  This  will  at 
once  modify  the  former  orbit  of  the  earth,  and  the  change 
will  depend,  in  quantity,  upon  the  mass  of  the  new  planet ; 
and  in  case  it  became  possible  to  measure  these  changes, 
their  values  will  give  the  weight  of  the  body  producing 
them. 

The  same  hypothesis  remaining  with  reference  to  the 
earth's  orbit,  we*  may  imagine  the  new  planet  to  revolve 
in  the  orbit  of  Venus,  interior  to  that  of  the  earth,  and 
the  same  kind  of  investigation  will  lead  to  the  determina- 
tion of  the  mass  of  this  interior  planet. 

We  shall  see  hereafter  that  certain  periodical  comets, 
favorably  located,  furnish  the  means  of  corroborating  the 
results  reached  by  the  above  train  of  reasoning,  by  the 
data  their  perturbations  furnish  for  reaching  the  mass  of 
the  planet  producing  these  effects. 

To  WEIGH  THE  SATELLITES. — The  effect  produced  by 
the  moon  on  the  earth  in  causing  the  figure  of  its  orbit 
to  sway  to  and  fro  under  the  moon's  attractive  power 
furnishes  again  the  data  whereby  the  moon's  mass  may 
be  determined.  In  the  case  of  many  satellites  to  the 
same  planet,  their  effects  on  each  other  being  carefully 
determined,  furnish  the  means  of  computing  their  masses. 
This,  however,  is  a  difficult  problem,  and  one  in  which  a 


INSTRUMENTAL    ASTRONOMY.  217 

solution  has  been  effected  only  in  the  system  of  Jupiter. 
The  masses  of  the  satellites  of  the  other  superior  planets 
have  as  yet  not  been  obtained  with  any  reliable  cer- 
tainty. 

We  have  thus  presented  methods  by  which  the  masses 
of  the  sun,  planets  and  satellites  may  be  obtained,  pro- 
vided certain  measurements  can  be  made,  which  measure- 
ments demand  the  aid  of  powerful  and  accurate  instru- 
ments. 

The  distances  separating  the  sun  and  planets,  and 
separating  the  primaries  and  their  satellites,  must  be 
obtained  before  we  can  trace  the  history  of  any  one  of 
these  revolving  worlds.  We  have  already  explained  the 
processes  by  which  the  earth's  distance  from  the  sun  may 
be^  obtained  by  the  use  of  the  phenomena  attending  the 
transit  of  Venus.  This  problem  again  demanded  instru- 
mental measurement.  Admitting  the  earth's  distance 
from  the  sun  to  be  known,  Kepler's  third  law  will  give 
the  distances  of  all  the  planets  of  our  system,  provided 
we  have  obtained  their  periods  of  revolution  around  the 
sun.  The  method  of  obtaining  the  periodic  times  has 
also  been  explained,  and  in  this  process  instrumental 
measurements  are  demanded. 

In  like  manner,  to  reach  the  periods  and  distances 
of  the  satellites,  their  elongations,  occultations  and 
eclipses,  must  be  carefully  measured  and  noted,  demand- 
ing instruments  of  a  high  order. 

To  trace  a  planet  or  satellite,  in  addition  to  the  quan- 
tities already  pointed  out,  we  have  seen  that  we  must 
know  the  intensity  of  the  impulsive  force  by  which  it 
was  projected  in  its  orbit.  But  we  have  seen  that  the 
intensity  of  any  impulse  is  measured  by  the  velocity  it  is 
capable  of  producing  in  a  unit  of  time.  Admitting, 


218  INSTRUMENTAL    ASTEONOMT. 

then,  that  we  know  the  distance  of  a  planet  from  the 
sun,  and  its  period  of  revolution,  we  know  the  velocity 
with  which  it  moves,  in  case  its  orbit  be  circular.  The 
earth,  for  example,  in  365£  days  accomplishes  a  jour- 
ney round  the  sun  in  a  circle  whose  diameter  is 
190.000,000,  and  whose  circumference  is  equal  to  this 
quantity  taken  3.14156  times.  Hence,  by  dividing  the 
number  of  miles  traveled  in  the  entire  circuit  by  the 
number  of  days  occupied  in  the  journey,  we  have  the  rate 
per  diem,  or  velocity.  Dividing  the  space  passed  over 
in  one  day  by  24,  we  have  the  rate  per  hour,  and  finally 
may  obtain  the  rate  per  second.  If  the  orbit  be  not 
circular,  we  can  always  find  a  circle  which,  for  a  very 
short  distance,  will  coincide  with  an  elliptic  or  other 
curve,  and  on  this  circle  we  may  suppose  the  planet  to 
move  for  a  very  short  time,  as  one  second,  with  uniform 
velocity,  and  the  space  passed  over  in  this  unit  will 
again  measure  the  intensity  of  the  impulsive  force  at  this 
part  of  the  orbit.  Here  again  we  have  presupposed  a 
knowledge  of  the  magnitude  and  figure  of  the  elliptic 
orbit  before  the  intensity  of  the  impulsive  force  can  be 
reached,  and  to  determine  these  quantities  instrumental 
measurement  is  demanded,  requiring  instruments  of  great 
perfection. 

The  last  quantity  demanded  by  the  mathematician  in 
writing  out  the  history  of  a  planet  moving  in  space  is 
the  direction  of  the  impulsive  force  projecting  it  in  its 
orbit.  This  is  readily  obtained  when  we  shall  have 
learned  the.  exact  direction  of  a  line  tangent  to  any  point 
of  the  planetary  orbit ;  for  the  direction  of  the  impulse 
must  always  be  tangent  to  the  curve  described  by  the 
body  set  in  motion.  If  we  join  the  planet  with  the  sun 
by  a  right  line,  this  line  will  form  an  angle  with  tangent 


INSTRUMENTAL    ASTRONOMY.  219 

to  the  planetary  orbit;  and  we  shall  find  hereafter  that 
the  nature  of  the  orbit  will  depend  upon  the  value  of  this 
angle,  or  in  other  language,  on  the  direction  in  which 
the  impulse  is  applied. 

Thus  we  find  that  not  a  single  quantity  of  the  five 
required  to  determine  the  circumstances  of  motion  of  a 
body  revolving  under  the  laws  of  motion  and  gravitation 
can  be  reached  without  instrumental  measurement ;  so 
that  our  entire  knowledge  of  the  physical  universe  hangs 
at  last  on  the  accuracy  and  perfection  of  the  instruments 
which  have  been  invented  and  constructed  for  making 
these  measures,  a  fact  which  elevates  instrumental  as- 
tronomy to  a  position  of  the  highest  dignity  and  im- 
portance. 

The  measures  demanded  in  instrumental  astronomy  are 
divided  into  two  great  classes.  In  the  first  class  all  the 
measures  of  position  are  absolute,  that  is,  a  star  or  planet 
whose  place  is  thus  determined  is  located  on  the  celes- 
tial sphere,  and  fixed  for  the  moment  in  position  by  a 
measure  of  its  distance,  say,  from  the  north  pole  of  the 
heavens  along  the  arc  of  a  great  circle,  and  also  its  dis- 
tance measured  on  the  equinoctial  from  the  vernal  equi- 
nox, or  from  some  other  fixed  points  which  may  have 
been  selected.  In  the  second  class  all  the  measures  are 
relative  or  differential ;  that  is,  an  interval  between  two 
points  in  close  proximity  is  determined.  To  this  class 
belong  the  measures  of  the  diameters  of  the  sun  and 
moon  and  planets ;  the  elongations  of  the  satellites  from 
their  primaries ;  the  measures  of  the  transits  of  Venus 
and  Mercury  across  the  disk  of  the  sun ;  the  measures  of 
the  solar  and  lunar  spots ;  the  distances  between  the 
double  and  multiple  stars ;  in  short,  all  those  measures 
involving  mere  differences  of  position. 


220  INSTRUMENTAL    ASTRONOMY. 

Each  of  these  classes  of  measures  demands  its  own 
peculiar  and  appropriate  instruments,  each  of  them  in- 
volving the  data  required  in  the  solution  of  the  subliinest 
problems  of  celestial  science. 

We  shall  now  proceed  to  exhibit  an  outline  of  the 
structure  of  a  few  of  the  most  important  instruments  be- 
longing to  these  two  classes,  only  for  the  purpose  of  pre- 
senting the  extraordinary  difficulties  which  must  be 
met  and  conquered  in  the  seemingly  simple  mechanical 
problem  of  fixing  the  place  of  a  star  in  the  celestial 
sphere. 

For  the  purpose  of  giving  position  to  the  heavenly 
bodies  astronomers  refer  them  to  the  surface  of  a  celes- 
tial sphere,  whose  poles  are  the  points  in  which  the 
earth's  axis  prolonged  pierces  the  sphere  of  the  fixed 
stars.  To  determine  a  point  on  the  surface  of  any 
sphere  we  must  fix  its  distance  on  the  arc  of  a  great 
circle  from  the  north  pole,  and  we  must  also  know  the 
distance  of  the  meridian  line  on  which  it  is  located,  from 
a  fixed  meridian. 

Astronomers  have  chosen  for  their  prime  meridian  that 
one  which  passes  through  the  vernal  equinox,  and  as  the 
celestial  sphere  revolves  to  our  senses  with  uniform  velo- 
city once  in  twenty-four  hours,  the  vernal  equinox  will 
come  at  the  end  of  this  period  to  the  meridian  of  the 
place  from  whence  it  started.  Any  object,  therefore, 
which  crosses  the  meridian  of  a  given  place  an  hour 
later  than  the  vernal  equinox  has  its  place  fixed  some- 
where on  the  circumference  of  a  known  meridian,  or 
hour  circle.  If  at  the  same  time  its  distance  from  the 
north  pole  can  be  determined,  its'  position  on  the  celes- 
tial sphere  will  be  positively  defined  by  these  two  ele- 
ments. As  we  have  already  seen,  the  vernal  equinox  is 


INSTRUMENTAL  ASTRONOMY.     221 

the  point  in  which  the  great  circle  of  the  heavens,  cut 
out  by  the  indefinite  extension  of  the  plane  of  the  earth's 
orbit,  intersects  the  equinoctial  circle,  or  that  circle  cut 
from  the  celestial  sphere  by  the  indefinite  extension  of 
the  plane  of  the  earth's  equator.  If  the  vernal  equinox 
were  absolutely  fixed,  and  if  in  that  point  a  star  were  lo- 
cated, this  star  would  revolve  with  all  the  other  stars  of 
the  heavens  once  in  twenty-four  sidereal  hours.  To 
mark  the  movement  of  this  vernal  equinox  astronomers 
employ  the  sidereal  clock,  whose  dial  is  divided  into 
twenty-four  hours,  and  which,  when  perfectly  adjusted, 
will  mark  Oh.  Om.  Os.  at  the  moment  the  vernal  equinox 
is  on  the  meridian  of  the  place  where  the  clock  is  located. 
All  points  on  the  celestial  sphere  will  pass  the  meridian 
necessarily  at  intervals  of  time  marking  the  position  of 
the  hour  circle  in  which  they  are  located,  relative  to  the 
prime  meridian  passing  through  the  vernal  equinox, 
These  intervals  of  time  which  elapse  between  the  passage 
of  the  vernal  equinox  across  the  meridian  of  a  given  place, 
and  the  passage  of  any  heavenly  body  across  the  same 
meridian,  are  called  right  ascensiojis.  Thus  a  star 
which  follows  the  vernal  equinox,  after  an  interval  of 
2h.  10m.  20s.,  as  marked  by  a  perfect  sidereal  clock,  has 
a  right  ascension  of  2h.  10m.  20s. 

Thus,  to  fix  the  place  of  any  heavenly  body  on  the 
celestial  sphere,  two  instruments  have  been  devised,  the 
one  having  for  its  object  to  measure  north  polar  dis- 
tances, while  the  other  is  employed  in  the  measurement 
of  right  ascensions  ;  the  first  of  these  is  denominated  a 
mural  circle,  while  the  second  is  called  a  transit  in- 
strument. 

We  shall  first  consider  the  principles  involved  in  the 
construction  of  the  transit  instrument.  This  instrument 


222        INSTRUMENTAL     ASTRONOMY. 

consists  of  a  telescope  mounted  upon  an  axis  perpendicu- 
lar to  the  axis  of  the  tube  of  the  telescope.  This  per- 
pendicular axis  terminates  at  each  extremity  in  two 
pivots  of  equal  size  and  perfectly  cylindrical  in  form. 
To  give  support  to  this  instrument  a  solid  pier  of  masonry 
is  built,  resting  upon  a  firm  foundation,  and  isolated  from 
the  surrounding  building.  On  the  upper  surface  of  this 
stone  pier  two  stone  columns  are  placed,  whose  centers 
are  separated  by  a  distance  equal  to  the  length  of  the 
axis  of  the  transit ;  on  the  tops  of  these  columns  metallic 
plates  are  fastened,  to  which  metal  pieces  are  attached, 
cut  into  the  shape  of  the  letter  Y.  If  in  these  Y's  the 
pivots  of  the  transit  be  laid,  in  case  the  axis  be  precisely 
level,  and  lying  due  east  and  west,  then  the  axis  of  the 
telescope,  or  visual  ray,  being  carried  around  the  heavens, 
by  revolving  the  instrument  in  its  Y's,  will  describe  a 
meridian  line  which  will  pass  through  the  north  pole  of 
the  heavens.  If  this  meridian  line  could  be  rendered 
visible  it  would  be  possible  to  note  the  passage  of  any 
star  or  other  heavenly  body  across  this  visible  meridian. 
This  cannot  be  accomplished  directly,  but  the  same  end 
is  reached  by  stretching  a  delicate  filament  of  spider's 
web  across  the  center  of  a  metallic  ring,  and  placing  it  in 
the  focus  of  the  eye-piece  of  the  telescope;  when  this 
spider's  web  is  lighted  up  by  a  lamp,  through  a  suitable 
orifice,  it  is  seen  as  a  delicate  golden  line  of  light  stretch- 
ing across  the  field  of  view,  and  resting  on  the  dark  back- 
ground of  the  heavens.  Revolving  the  ring  which  bears 
the  spider's  web,  we  may  bring  this  web  to  coincide, 
throughout  its  entire  length,  with  a  true  meridian  line, 
and  thus,  in  reality,  we  procure  for  ourselves  a  visible 
meridian  quite  as  perfect  for  our  purposes  as  though  it 
were  an  actual  line  of  light,  sweeping  from  north  to  south 


INSTRUMENTAL     ASTRONOMY.         223 

across  the  celestial  sphere.  To  render  visible  the  axis 
of  the  telescope,  or  to  direct  the  visual  ray,  another 
spider's  web  is  stretched  across  the  field  of  view,  in  di- 
rection perpendicular  to  the  first,  and  precisely  in  the 
center  of  the  field,  so  that  by  their  intersection  these 
spiders'  webs  form  a  point  of  almost  mathematical  mi- 
nuteness. 

Let  us  now  examine  what  is  demanded  in  the  construc- 
tion of  the  transit  to  render  it  an  instrument  perfect  in 
performance.  The  object-glass  and  the  eye-piece,  form- 
ing the  optical  portion  of  the  telescope,  should  be  per- 
fect in  their  figure  and  adjustments ;  the  tube  in  which 
they  are  placed  should  be  perfectly  rigid  and  inflexible  ; 
the  optical  axis  or  line  of  collimaliou  should  be  exactly 
perpendicular  to  the  horizontal  axis  on  which  the  instru- 
ment revolves ;  the  pivots  should  be  exactly  equal  to 
each  other,  and  precisely  cylindrical  in  form ;  the  hori- 
zontal axis  should  lay  in  a  direction  exactly  east  and 
west,  and  should  be  absolutely  level.  In  connection  with 
the  transit  we  require  a  perfect  time-keeper.  The  clock, 
when  properly  adjusted,  will  mark  Oh.  00m.  OOs.  at  the 
moment  the  vernal  equinox  is  seen  to  pass  the  visible 
spider's  line  meridian  of  the  telescope  ;  it  must  then 
move  uniformly  during  the  entire  revolution  of  the  heav- 
ens, and  mark  the  zero  of  time  again  when  the  vernal 
equinox  returns  to  the  meridian  line.  Such  are  the  me- 
chanical demands  required  in  the  construction  and  use  of 
the  transit  and  clock ;  but  to  obtain  a  perfect  result  the 
observer  is  required  to  perform  his  part  in  the  operation ; 
he  must  note  the  exact  instant  at  which  the  vernal  equi- 
nox passes  the  visible  meridian,  so  as  to  set  his  sidereal 
clock ;  this  being  accomplished,  to  obtain  the  right  ascen- 
sion of  any  heavenly  body  he  must  seize  the  precise  ino- 


224        INSTRUMENTAL     ASTRONOMY. 

ment,  as  marked  by  his  clock,  at  which  the  center  of  the 
object  under  observation  passes  the  meridian. 

To  obtain,  then,  the  element  of  right  ascension,  required 
to  fix  the  place  of  a  heavenly  body  at  a  given  moment,  we 
require  a  perfect  transit,  perfectly  adjusted,  a  perfect 
clock,  perfectly  rated,  and  a  perfect  observer,  with  a  per- 
fect method  of  subdividing  time  into  minute  fractions. 
Not  one  single  one  of  these  demands  can  ever  be  met. 
Even  admitting  the  possible  construction  of  a  perfect  in- 
strument, every  change  of  temperature  will  effect  certain 
changes  in  the  material  of  which  it  is  composed  No 
two  pivots  can  possibly  be  made  exactly  equal,  nor  pre- 
cisely cylindrical  in  form ;  and  should  the  observer  suc- 
ceed in  placing  the  axis  of  his  transit  so  as  to  lie  east 
and  west,  as  well  as  horizontal,  it  will  not  remain  in  this 
position  for  even  a  single  hour  of  time.  If  the  clock  be 
adjusted  so  as  to  mark  the  exact  zero  of  time,  and  to 
move  off  with  a  uniform  rate,  this  rate  will  soon  sensibly 
change,  and  must  be  carefully  watched  even  from  hour 
to  hour.  The  observer  himself  is  but  an  imperfect  and 
variable  machine,  utterly  incapable  of  marking  the  exact 
moments  required,  his  work  being  subject  to  errors, 
whose  values  fluctuate  from  day  to  day  ;  and  to  add  to 
all  these  difficulties,  the  atmosphere  which  surrounds  the 
earth  not  only  possesses  the  power  of  diverting  the  rays 
of  light  from  their  rectilineal  path,  but  because  of  its  con- 
stant fluctuations  and  changes  produces  a  tremulous  or 
dancing  motion  in  the  stars 'under  observation  which,  to 
a  certain  extent,  renders  it  impossible  to  do  exact  work, 
even  with  perfect  instruments  and  perfect  observers,  could 
such  be  found. 

We  will  now  examine  the  instrumental  means  required 
to  determine  the  second  element,  the  north  polar  dis- 


INSTRUMENTAL    ASTRONOMY.  225 

tance,  which  is  demanded  in  fixing  the  place  of  a 
heavenly  body.  For  this  purpose  let  us  suppose  a  metal- 
lic circle  to  be  permanently  fastened  to  the  horizontal 
axis  of  the  transit,  having  its  center  in  the  central  line 
of  the  axis,  and  its  plane  perpendicular  to  this  line.  Let 
us  suppose  the  rim  of  this  circle  to  be  divided  into  de- 
grees, minutes  and  seconds  of  arc,  and  this  division  to 
have  been  perfectly  accomplished.  Let  us  direct  the 
transit  telescope  precisely  to  the  north  pole  of  the 
heavens,  and  when  thus  directed  let  us  fix  upon  the  stone 
pier  a  permanent  mark  or  pointer,  directed  to  the  zero 
point  on  the  divided  circle.  As  we  turn  the  transit  away 
from  the  north  pole  toward  the  south  the  zero  point  on 
the  circle  will  in  like  manner  leave  the  fixed  pointer,  and 
thus  the  distance  from  the  north  pole  to  any  object  to 
which  the  telescope  may  be  directed  will  be  read  on  the 
divided  circle  from  the  zero  round  to  the  division  to 
which  the  pointer  directs.  Such  an  instrument  is  called 
a  meridian  circle.  Here  again  new  mechanical  diffi- 
culties present  themselves.  The  centering  of*  the  circlej 
the  perfection  of  the  divisions  upon  its  circumference,  are 
matters  which  cannot  be  accomplished  with  absolute  ac- 
curacy ;  and  even  if  this  were  possible,  they  are  liable  to 
changes  to  which  all  material  is  subjected  at  every  mo- 
ment. The  same  is  true  of  the  stability  of  the  pointer, 
any  change  in  whose  position  must  involve  an  error  in 
the  measured  north  polar  distance. 

Thus  far  we  have  supposed  that  in  our  celestial  sphere 
we  have  two  fixed  points  of  reference,  namely,  the  ver- 
nal equinox  and  the  north  polar  point.  Unfortunately 
for  the  observer,  and  to  increase  the  difficulties  by  which 
he  is  surrounded,  neither  of  these  points  remains  abso- 
lutely fixed,  and  even  their  rate  of  movement  is  not  uni- 
10* 


226  INSTRUMENTAL    ASTRONOMY. 

form ;  and  thus  one  difficulty  rises  above  another,  cul- 
minating in  the  fact  that  even  the  light  whereby  objects 
become  visible  does  not  dart  through  space  with  infinite 
velocity,  but  wings  its  flight  with  a  measurable  speed, 
which,  when  conjoined  with  the  speed  of  the  earth's  re- 
volution in  its  orbit,  sensibly  changes  the  apparent  place 
of  every  object  under  examination.  Add  to  this  long 
catalogue  of  difficulties  the  fact  that  the  earth's  rotation  on 
its  axis  is  rapidly  revolving  the  observer,  his  instruments 
and  observatory,  at  a  possible  rate  of  a  thousand  miles  an 
hour,  and  some  idea  may  be  formed  of  the  embarrassments 
under  which  astronomers  are  compelled  to  work  out  the 
resolution  of  the  great  problems  of  the  heavens. 

Having  presented  this  array  of  difficulties,  we  shall 
not  undertake  to  show  in  every  instance  by  what  precise 
means  they  are  overcome.  So  far  as  regards  the  move- 
ment of  the  vernal  equinox  and  the  north  pole,  the  most 
extended  and  elaborate  observations  have  been  made 
through  a  long  series  of  years  by  the  best  instruments 
and  the  most  skillful  observers,  and  these  have  been  re- 
duced and  discussed  by  the  most  able  mathematicians, 
until  by  different  methods  astronomers  have  reached  to  so 
perfect  a  knowledge  of  the  values  of  the  errors  due  to 
these  two  causes  that  it  seems  as  though  no  greater  ap- 
proximation to  accuracy  can  be  made  by  the  same  methods. 
That  correction  due  to  the  movement  of  the  vernal  equi- 
nox is  called  precession  ;  that  due  to  the  movement  of  the 
north  pole  is  called  nutation,  of  which  we  shall  give 
more  accurate  account  hereafter.  The  error  arising  from 
the  velocity  of  light,  combined  with  the  orbital  and  ro- 
tary motion  of  the  earth,  is  called  aberration.  This 
subject  will  also  be  treated  hereafter.  Of  the  three 
principal  instrumental  errors,  that  arising  from  want  of 


INSTRUMENTAL    ASTRONOMY.  227 

exact  perpendicularity  in  the  position  of  the  axis  of  the 
telescope  to  the  horizontal  axis  of  the  transit  is  called  the 
collimation  error,  and  may  be  detected  and  measured  by 
mechanical  means  ;  its  effect  is  to  cause  the  visual  ray  to 
pierce  the  heavens  east  or  west  of  the  true  meridian,  and 
in  the  revolution  of  the  transit  this  point  of  piercing  will 
describe  a  small  circle  of  the  sphere,  instead  of  the  great 
meridian  circle,  which  it  ought  to  describe.  The  error 
arising  from  a  failure  to  place  the  transit  axis  in  a  truly 
horizontal  position  is  called  the  level  error ;  its  effect  is 
to  cause  the  visual  ray  to  pierce  the  heavens  east  or  west 
of  the  true  meridian,  and  the  point  of  piercing,  by 
the  revolution  of  the  transit  on  its  axis,  will  describe 
a  great  circle  of  a  sphere  inclined  to  the  true  meridian, 
under  an  angle  equal  to  that  which  the  axis  of  the  tran- 
sit makes  with  the  horizon,  or  equal  to  the  level  error. 
The  failure  to  place  the  axis  of  the  transit  precisely 
east  and  west  gives  rise  to  what  is  called  the  azimuthal 
error.  This  causes  the  visual  ray  or  line  of  collimation 
of  the  telescope  to  pierce  the  heavens  on  the  true  meri- 
dian only  when  directed  to  the  zenith.  This  point  of 
piercing,  by  revolving  the  transit  on  its  axis,  describes  a 
great  circle,  which  departs  from  the  true  meridian  at  the 
zenith,  under  an  angle  precisely  equal  to  the  azimuthal 
error.  Methods  have  been  devised  for  measuring  these 
various  errors,  and  for  computing  their  effect  upon  the 
apparent  places  of  the  heavenly  bodies. 

The  rays  of  light  by  which  every  object  is  rendered 
visible,  as  we  have  already^  stated,  on  entering  the  earth's 
atmosphere  are  bent  from  their  rectilineal  path,  giving 
rise  to  a  source  of  error  called  refraction.  The  laws 
governing  the  direction  of  the  light,  as  affected  by  the 
atmosphere,  have  been  carefully  studied,  so  that  at 


228  INSTRUMENTAL    ASTRONOMY. 

present  it  is  possible  to  compute  with  great  exactitude 
the  change  of  place  of  any  object  under  observation  due 
to  the  effects  of  refraction.  The  flexure  of  the  tube  of 
the  telescope,  under  the  various  circumstances  by  which 
it  may  be  surrounded,  have  been  thoroughly  investigated, 
while  the  exact  figure  of  the  pivots  of  the  axis  has  been 
subjected  to  the  most  rigorous  mechanical  tests  ;  in  short, 
all  the  mechanical  deficiencies  in  the  instrument  have 
occupied  the  attention  of  many  of  the  best  minds  for  the 
past  two  hundred  years,  and  thus  slow  but  steady  ad- 
vances in  accuracy  have  been  accomplished. 

To  remedy  the  errors  arising  from  the  perturbations  of 
the  atmosphere,  as  well  as  those  arising  from  personal 
error  in  the  observer,  in  seizing  the  moment  of  transit 
across  the  visible  meridian  line,  several  spider's  lines, 
commonly  called  wires,  parallel  to  each  other,  have  been 
introduced  into  the  focus  of  the  eye-piece  of  the  transit, 
and  thus  the  instant  at  which  the  star  passes  each  one 
of  these  wires  being  noted  as  accurately  as  possible,  the 
average  of  all  gives  a  better  result  than  could  have  been 
obtained  from  any  one  wire. 

To  remedy  the  defects  arising  from  the  imperfect 
divisions,  from  imperfect  centering,  and  from  changes  of 
figure  in  the  circle  from  whence  the  north  polar  dis- 
tances are  read,  it  is  usual  to  have  four  pointers,  and 
even  sometimes  six,  by  means  of  which  the  north  polar 
distance  is  read  in  as  many  places  on  the  divided  circle, 
the  average  of  all  giving  a  better  result  than  any  one 
reading.  These  pointers,  as  w^  have  named  them,  are  in 
eality  powerful  microscopes,  permanently  fixed  in  the 
heavy  stone  pier,  on  which  the  instrument  rests,  and 
having  their  visual  ray  fixed  by  the  intersection  of 
spiders'  webs,  as  in  the  principal  telescope. 


INSTRUMENTAL     ASTRONOMY.          229 

From  these  instrumental  imperfections  we  pass  to  those 
which  belong  to  the  clock,  and  here  again  we  are  com- 
pelled to  work  with  an  imperfect  machine.  No  clock  has 
ever  been  made  which  can  keep  perfect  time,  and  the 
great  object  of  the  observer  is  to  learn  the  peculiarities 
of  his  clock,  to  determine  its  deviations  from  absolute 
accuracy,  and  to  be  able  to  mark  these  deviations,  if  pos- 
sible, from  minute  to  minute. 

The  observer,  having  mastered  all  the  sources  of  error 
above  described,  next  comes  to  the  consideration  of  his 
own  personal  deviations  from  accuracy  in  attempting  to 
mark  the  moment  at  which  a  star  crosses  his  visible  me- 
ridian. To  observe  the  transit  of  a  star  across  the  meri- 
dian, he  places  himself  at  the  transit  instrument,  enters  in 
his  note-book  the  hour  and  minute  from  the  face  of  the  clock, 
then  fixing  his  eye  through  the  telescope  upon  the  star, 
and  counting  the  beats  of  the  pendulum,  he  follows  the 
star  as  it  slowly  advances  to  the  meridian  wire.  Between 
somB  two  beats  thus  counted  the  star  crosses  the  wire. 
The  observer  holds  in  his  mind,  as  well  as  he  can,  the 
star's  position  at  the  close  of  the  beat  before  the  passage, 
and  at  the  close  of  the  next  beat  after  the  passage,  and 
mentally  subdividing  this  space  passed  over  in  one  second 
into  ten  equal  parts,  he  estimates  how  many  of  these 
parts  precede  the  passage  of  the  star  across  the  meri- 
dian, and  these  parts  are  the  fractions  or  tenths  of  a 
second,  which  mark  the  time  of  transit.  Thus  he  adds 
to  the  entry  in  his  note-book  already  made  the  number 
of  beats  of  the  pendulum  and  also  the  fractions  of  a 
second  above  obtained,  and  thus  the  time  of  transit  is 
obtained,  approximately  to  the  tenth  part  of  one  second 
of  time. 

In  the  method  of  observing  transits  just  explained  so 


230    INSTRUMENTAL  ASTRONOMY. 

many  things  are  demanded  of  the  observer  that  his  atten- 
tion cannot  be  given  exclusively  to  the  determination  of 
the  moment  of  transit ;  he  must  keep  up  the  count  of  the 
clock  beat ;  he  must  hold  in  his  mind  the  interval  passed 
over  by  the  star  from  one  beat  to  the  next  during  the 
transit;  he  must  divide  this  space  by  estimation  into 
tenths •  /  he  must  assign  the  number  of  tenths  which  pre- 
cede the  transit ;  he  must  enter  the  seconds  and  tenths  in 
his  note-book,  keeping  up  the  count  of  the  beats  of  the 
pendulum,  and  thus  pass  from  one  wire  to  the  next  suc- 
cessively through  all  the  system  of  wires,  so  that  in  this 
multiform  effort  his  powers  of  attention  are  taxed  beyond 
what  they  are  able  to  bear,  and  it  is  only  by  long  prac- 
tice that  any  valuable  results  are  ever  reached.  The  ob- 
server also  finds  that  his  modes  of  observation  often  lead 
him  into  false  habits.  He  may  mark  the  time  from  his 
own  mental  count  of  the  beat,  rather  than  from  the 
sound  of  the  beat  itself,  or  he  may  find  himself  running 
into  the  habit  of  fixing  his  tenths  of  seconds  predominantly 
in  one  or  two  portions  of  the  scale  of  tenths.  It  is 
manifest  that  in  a  thousand  observations  the  tenth  of  a 
second  on  which  the  transit  falls  ought  to  be  uniformly 
divided  among  the  whole  number.  Thus  there  should  be 
a  hundred  observations  in  which  the  time  of  transit 
should  fall  on  the  first  tenth  of  a  second,  a  hundred  ob- 
servations in  which  the  time  should  fall  on  the  second 
tenth,  and  so  on  for  each  of  the  tenths.  But  an  observer 
may  find  when  he  comes  to  examine  a  thousand  of  his  ob- 
servations that  two  or  three  hundred  are  entered  as  fall- 
ing on  the  third  tenth,  and  three  or  four  hundred  as 
falling  on  the  seventh  tenth.  This  only  demonstrates 
that  he  has  fallen  into  habitual  error,  due  to  the  fact 
that  he  is  compelled  to  estimate.  In  attempting  to 


INSTRUMENTAL  ASTRONOMY.     231 

escape  from  this  particular  error,  and  finding  himself  too 
much  attached  to  one  portion  of  his  scale  of  tenths,  he  is 
very  likely  to  fall  into  the  other  extreme,  and  thus  he 
finds  himself  a  variable  instrument,  always  imperfect, 
even  in  these  legitimate  sources  of  error. 

By  studying  his  own  peculiarities  more  rigorously,  and 
comparing  himself  with  others,  it  will  be  found  that  in 
case  the  two  persons  compared  could  at  the  same  time 
look  through  the  same  telescope  at  the  same  star  coming 
up  to  cross  the  same  meridian  wire,  each  attempting  to 
note  the  moment  of  passage,  by  listening  to  the  beat  of 
the  same  clock,  the  recorded  times  would  differ,  one  of 
the  observers  being  uniformly  in  advance  of  the  other. 
Should  this  experiment  be  repeated,  at  the  end  of  a 
month,  with  every  possible  precaution,  the  difference  be- 
tween the  two  observers  will  in  general  be  found  to 
change,  demonstrating  that  one  or  the  other  or  both  have 
varied  in  this  particular,  and  that  an  inter-comparison 
of  their  observations  now  made  by  the  former  difference 
would  produce  inaccurate  results.  This  difference  is  what 
is  denominated  technically  personal  equation,  and  is  sup  • 
posed  to  arise  from  the  fact  that  time  is  really  an  ele- 
ment in  the  operation  of  the  senses :  that  two  persons 
listening  to  the  same  sound,  as  the  sharp  crack  of  a  pis- 
tol, the  sense  of  hearing  of  the  one  may  perform  its  office 
of  conveying  this  sound  to  the  brain  more  rapidly  than 
the  other,  and  that  the  same  may  be  asserted  of  the  sense 
of  sight. 

For  the  purpose  of  comparing  the  observations  of  dif- 
ferent astronomers,  it  becomes  necessary  to  determine  the 
peculiarities  of  each,  and  it  would  be  a  matter  of  great 
importance  if  it  were  possible  to  fix  some  absolute  stand- 
ard to  which  all  observations  might  be  reduced.  This  is 


232         INSTRUMENTAL     ASTRONOMY. 

accomplished,  so  far  as  the  three  instrumental  errors  and- 
the  clock  error  are  concerned,  by  actually  applying  a  cor- 
rection which  reduces  each  observation  to  what  it  would 
have  been  in  case  none  of  these  errors  had  existed.  The 
same  may  be  said  of  the  correction  applied  for  refraction 
and  for  aberration.  As  to  precession,  the  position  of  the 
equinoctial  point,  supposing  it  to  move  with  its  mean  or 
average  velocity,  is  always  given  for  the  epoch  to  which 
the  observation  is  referred.  The  observations  are  also 
reduced  for  parallax  whenever  this  element  becomes 
sensible,  and  are  thus  recorded  as  though  the  observer 
were  located  at  the  center  of  the  earth.  To  accomplish 
the  inter-comparison  of  observations  made  at  different  ob- 
servatories, there  yet  remains  the  reduction  due  to  differ- 
ence of  longitude,  and  that  depending  upon  the  personal 
peculiarities  of  the  observers. 

The  high  demand  for  accuracy  in  instrumental  obser- 
vation can  only  be  fully  appreciated  by  those  actually 
engaged  in  the  computation  of  the  places  of  the  heavenly 
bodies.  Observations  are  valuable  in  the  ratio  of  the 
squares  of  their  probable  errors :  that  is,  if  one  set  of 
observations  can  be  produced  in  which  the  probable 
errors  remain  among  the  tenths  of  seconds  of  time,  while 
in  another  set  of  observations  the  errors  are  driven  into 
the  hundredths  of  seconds,  or  are  but  one  tenth  part  as 
large  as  the  former,  then  the  second  set  will  be  a  hundred 
fold  more  valuable  than  the  first.  This  principle  applies 
to  all  observations,  but  there  are  some  distances  so  great 
and  some  motions  so  slow  that  even  the  best  and  most 
delicate  methods  of  observation  hitherto  applied  fail  alto- 
gether to  measure  the  one  or  to  appreciate  the  other. 
This  remark  is  especially  true  when  applied  to  the 
distance  and  movements  which  are  found  in  the  region 


INSTRUMENTAL    ASTRONOMY.  233 

of  the  fixed  stars.  Among  these  remote  objects,  while 
in  some  instances  the  motion  is  sufficiently  rapid  to  be 
detected  and  approximately  measured,  even  in  a  single 
year,  in  other  instances,  and  by  far  the  larger  number, 
these  motions  are  so  slow  that  they  must  accumulate  for 
hundreds  of  years  to  become  appreciable  and  measurable 
by  the  most  refined  and  perfect  instruments  hitherto  pre- 
pared by  human  skill. 

In  the  three  great  departments  of  astronomy  there  is 
but  one  in  which  there  is  much  hope  for  increased  facility 
and  accuracy.  The  great  laws  of  motion  and  gravitation 
are  no  doubt  perfectly  determined.  The  mathematical 
formulae  whereby  these  laws  are  applied  to  the  circum- 
stances of  motion  of  the  planets  and  their  satellites  are 
now  brought  to  great  simplicity  and  perfection ;  and  if  it 
were  possible  to  give  to  the  physical  astronomer  perfect 
data,  he  would  be  able  to  obtain  -perfect  results.  We 
know  by  geometry  that  the  area  of  a  rectangle  is  the  pro- 
duct of  its  base  by  its  altitude.  This  rule  or  formula  is  ab- 
solutely accurate,  and  whenever  we  wish  to  apply  it  to  de- 
termine the  area  of  any  particular  rectangle  we  must  first 
accomplish  the  mechanical  measurement  of  the  length  of 
the  base  and  altitude.  To  do  this  perfectly  is  impos- 
sible, but  approximate  results  may  be  reached  of  greater 
or  less  precision  in  proportion  to  the  accuracy  of  the  in- 
struments employed,  and  the  time  and  pains  expended 
upon  the  work.  Thus  one  measure  may  reduce  the  pro- 
bable errors  to  one  hundredth  of  an  inch,  while  in  another 
the  error  may  only  reach  one  thousandth  of  the  same 
unit. 

In  like  manner  the  theory  and  formulae  of  physical  as- 
tronomy are  nearly,  if  not  quite  perfect,  while,  however, 
the  observations  whence  we  derive  the  data  to  be  used  in 


234  INSTRUMENTAL    ASTRONOMY. 

computation  are,  as  we  have  seen,  comparatively  imper- 
fect. The  author  of  this  work  has  attempted  to  contri- 
bute something  to  the  accuracy  and  facility  of  astronomi- 
cal observation. 

The  following  is  a  brief  account  of  the  circumstances 
attending  the  invention  of  this  new  mode  of  observation, 
now  known  as 

THE  AMERICAN  METHOD  OF  TRANSITS. — In  the  autumn 
of  the  year  1848,  the  late  Professor  S.  C.  Walker,  then 
of  the  United  States  Coast  Survey,  was  engaged  with 
me  at  the  Cincinnati  Observatory  in  a  series  of  observa- 
tions, having  for  their  object  the  determination  of  the 
difference  of  longitude  between  the  observatories  of  Phila- 
delphia and  Cincinnati.  In  comparing  our  clocks  or 
chronometers  with  those  of  Philadelphia,  an  observer  at 
Philadelphia  listening  to  the  clock-beat  touched  the  mag- 
netic key  of  the  telegraph  wire  at  every  beat,  and  we  re- 
ceived at  Cincinnati  an  audible  tick  every  second  of 
time,  which  was  carefully  noted,  and  thus  our  clocks 
were  compared.  There  were  two  sources  of  error  in  this 
method  of  comparison,  arising  from  an  imperfect  imita- 
tion of  the  clock- beat  by  the  Philadelphia  operator,  also 
from  our  noting  the  arrival  of  that  beat  in  Cincinnati. 
On  the  26th  of  October,  1848,  Professor  Walker,  while 
conversing  on  this  subject,  first  presented  to  me  the  me- 
chanical problem  of  causing  the  clock  to  send  its  own 
beats  by  telegraph  from  one  station  to  the  other,  or 
what  amounted  to  the  same  thing,  the  problem  of  convert- 
ing time  into  space,  as  already  explained ;  for  in  case 
the  clock  could  send  its  own  beats  by  telegraph,  and 
these  beats  could  be  received  on  a  uniformly  flowing  time 
scale,  the  star  transit  could  be  also  sent  by  telegraph,  and 
received  on  the  same  scale ;  and  thus  a  new  method  of 


INSTRUMENTAL     ASTRONOMY.         235 

transits  would  at  once  spring  from  the  resolution  of  the 
first  mechanical  problem.  I  was  informed  by  Professor 
Walker  that  the  problem  had  already  been  presented  to 
others,  but,  so  far  as  he  knew,  had  never  been  solved. 
The  full  value  of  the  idea  was  at  once  appreciated ;  and 
on  the  same  evening  a  common  brass  clock,  the  only- 
one  then  in  the  observatory,  was  made  to  record  its  own 
beats  by  the -use  of  the  electro-magnet  on  a  Morse  fillet. 

The  problem  once  solved,  nothing  more  remained  than 
to  elaborate  such  machinery  as  would  render  it  possible 
to  apply  this  new  discovery  or  invention  to  the  delicate 
and  positive  demands  of  astronomical  observations. 

It  is  well  known  that  signals  are  transmitted  along  a 
line  of  telegraphic  wire  by  closing  or  by  breaking  the  wire 
circuit  over  which  the  electricity  passes  from  pole  to  pole 
of  the  battery.  The  finger  of  the  telegraphic  operator,  by 
touching  a  magnetic  key,  "  breaks  or  makes  "  the  circuit, 
and  thus  either  interrupts  or  starts  the  flow  of  electricity. 
The  problem  of  causing  a  clock  to  record  its  beats  tele- 
graphically was  then  nothing  more  than  to  contrive  some 
method  whereby  the  clock  might  be  made  (by  the  use  of 
some  portion  of  its  own  machinery)  to  take  the  place  of  the 
finger  of  the  living,  intelligent  operator,  and  "  make"  or 
<{  break"  the  electric  circuit.  The  grand  difficulty  did  not 
lie  in  causing  the  clock  to  play  the  part  of  an  automaton  in 
this  precise  particular,  but  it  did  lie  in  causing  the  clock  to 
act  automatically,  and  at  the  same  time  perform  perfectly 
its  great  function  of  a  time-keeper.  This  became  a  mat- 
ter of  great  difficulty  and  delicacy ;  for  to  tax  any  por- 
tion of  the  clock  machinery  with  a  duty  beyond  the  ordi- 
nary and  contemplated  demands  of  the  maker,  seemed 
at  onco  to  involve  the  machine  in  imperfect  and  irregular 
action.  After  due  reflection  it  was  decided  to  apply  to 


236        INSTRUMENTAL     ASTRONOMY. 

the  pendulum  for  a  minute  amount  of  power,  whereby  the 
making  or  breaking  the  electric  circuit  might  be  accom- 
plished with  the  greatest  chance  of  escaping  any  injurious 
effect  on  the  going  of  the  clock.  The  principle  which 
guided  in  this  selection  was,  that  we  ought  to  go  to  the 
prime  mover  (which  in  this  case  was  the  clock  weights, 
and  which  could  not  be  employed,)  and  failing  to  reach 
the  prime  mover,  we  should  select  the  nearest  piece  of 
mechanism  to  it,  which  in  the  clock  is  the  pendulum. 
A  second  point  early  determined  by  experiment  and  re- 
flection was  this  :  that  the  making  or  breaking  of  the  cir- 
cuit must  be  accomplished  by  the  use  of  mercury,  and 
not  by  a  solid  metallic  connection.  The  method  evolved 
and  based  on  these  two  principles  is  the  one  which  has 
been  in  use  now  for  more  than  ten  years  in  the  Cincin- 
nati Observatory. 

The  simplest  possible  method  of  causing  the  pendulum 
to  "  make  "  the  circuit  may  be  described  as  follows  : 

Attach  to  the  under  surface  of  the  clock  pendulum 

with  gum  shellac  a  small  bit  of  wire  bent  thus,  / ^ 

then  right  and  left  of  the  point  over  which  the  pendu- 
lum vibrates  when  lowest  place  two  small  globules  of 
mercury,  into  each  of  which  there  shall  dip  a  wire  from 
the  poles  of  the  battery.  Now,  as  the  pendulum  swings 
over  the  globules  of  mercury,  the  two  points  of  the  at- 
tached wire  will  finally  come,  for  one  moment,  to  dip  in 
the  mercury  cups,  and  thus  make  a  momentary  bridge, 
over  which  the  current  of  electricity  may  pass  from  pole 
to  pole.  This  method,  among  others,  having  been  tried, 
was  soon  abandoned  as  uncertain  and  irregular  in  its  re- 
sults ;  and  the  following  plan  was  adopted  : 

A  small  cross  of  delicate  wire  was  mounted  on  a  short 
axis  of  the  same  material,  passing  through  the  point  of 


INSTRUMENTAL    ASTRONOMY.  237 

union  of  the  four  arms  constituting  the  cross.  This  axis 
was  then  placed  horizontal  on  a  metallic  support,  in  Y's, 
where  it  might  vibrate,  provided  the  top  stem  of  the  cross 
could  be  in  some  way  attached  to  the  pendulum  of  the 
clock,  and  the  "  cross  "  should  thus  rise  and  fall  at  its 
outer  stem  as  the  pendulum  swings  backward  and  forward. 
The  metallic  frame  bearing  the  "cross"  also  bore  a 
small  glass  tube  bent  at  right  angles.  This  was  filled 
with  mercury,  and  into  one  extremity  one  wire  from 
the  pole  of  the  battery  was  made  to  dip ;  the  other 
wire  was  made  fast  by  a  binding  screw  to  the  metal- 
lic stand  bearing  the  "cross,"  and  thus  every  time  the 
"cross"  dipped  into  the  mercury  in  the  bent  tube,  the 
electricity  passed  through  the  metallic  frame,  up  the  ver- 
tical standards  bearing  the  axis  of  the  cross,  along  the 
axis  to  the  stem,  and  down  the  stem  into  the  mercury, 
and  finally  through  the  mercury  to  the  other  pole  of 
the  battery.  Thus  at  every  swing  .of  the  pendulum 
the  circuit  was  made,  and  a  suitable  apparatus  might, 
by  the  electro-magnet,  record  each  alternate  second  of 
time. 

The  amount  of  power  required  of  the  pendulum  to  give 
motion  to  the  delicate  wire-cross  was  almost  insensible, 
as  the  stems  nearly  counterpoised  each  other  in  every 
position.  Here,  however,  there  was  great  difficulty  in  pro- 
curing a  fibre  sufficiently  minute  and  elastic  to  consti- 
tute the  physical  union  between  the  top  stem  of  the 
cross  and  the  clock  pendulum.  Various  materials  were 
tried,  among  others  a  delicate  human  hair,  the  very  finest 
that  could  be  obtained,  but  this  was  too  coarse  and  stiff. 
Its  want  of  pliancy  and  elasticity  gave  to  the  minute 
"  wire-cross  "  an  irregular  motion,  and  caused  it  to  re 
bound  from  the  globule  of  mercury  into  which  it  should 


238  INSTRUMENTAL    ASTRONOMY. 

have  plunged.  After  many  fruitless  efforts,  an  appeal 
was  made  to  an  artisan  of  wonderful  dexterity ;  the  as- 
sistance of  the  spider  was  invoked;  his  web,  perfectly 
elastic  and  perfectly  pliable,  was  furnished,  and  this  ma- 
terial connection  between  the  wire-cross  and  the  clock 
pendulum  proved  to  be  exactly  the  thing  required.  In 
proof  of  this  remark  I  need  only  state  the  fact  that  one 
single  spider's  web  has  fulfilled  the  delicate  duty  of 
moving  the  wire-cross,  lifting  it,  and  again  permitting  it 
to  dip  into  the  mercury  every  second  of  time  for  a  period 
of  more  than  three  years  1  How  much  longer  it  might 
have  faithfully  performed  the  same  service  I  know  not, 
as  it  then  became  necessary  to  break  this  admirable 
bond,  to  make  some  changes  in  the  clock.  Here  it  will 
be  seen  the  same  web  was  expanded  and  contracted 
each  second  during  this  whole  period,  and  yet  never,  so 
far  as  could  be  observed,  lost  any  portion  of  its  elasticity. 
The  clock  was  thus  made  to  close  the  electric  circuit  in 
the  most  perfect  manner;  and  inasmuch  as  the  resistance 
opposed  to  the  pendulum  by  the  "  wire-cross  "  was  a 
constant  quantity  and  very  minute,  thus  acting  pre- 
cisely as  does  the  resistance  of  the  atmosphere,  the 
clock,  once  regulated  with  the  "  cross  "  as  a  portion  of 
its  machinery,  moved  with  its  wonted  steadiness  and 
uniformity.  Thus  one  grand  point  was  gained.  The 
clock  was  now  ready  to  record  its  own  beats  automati- 
cally and  with  absolute  certainty,  without  in  any  way 
affecting  the  regularity  of  its  movement.  It  was  early 
objected  to  the  mercurial  connection  just  described,  that 
in  a  short  time  the  surface  of  the  mercury  would  be- 
come oxidized,  and  thus  refuse  to  transmit  the  current 
of  electricity ;  but  experiment  demonstrated  that  the  ex- 
plosion produced  by  the  electric  discharge  at  every  dip 


INSTRUMENTAL    ASTRONOMY.  239 

into  the  mercury  threw  off  the  oxide  formed,  and  left  the 
polished  surface  of  the  globule  of  mercury  in  a  perfect 
state  to  receive  the  next  passage  of  the  electricity. 

So  far  as  known,  all  other  methods  are  now  abandoned, 
and  the  mercurial  connection  is  the  only  one  in  use. 

THE  TIME  SCALE. — The  clock  being  now  prepared  to 
record  its  beats,  accurately  and  uniformly,  the  next  im- 
portant step  was  to  obtain,  if  possible,  a  uniformly  moving 
time-scale,  which  should  be  applicable  to  the  practical 
demands  of  the  astronomer. 

In  case  the  fillet  of  paper  used  in  the  Morse  telegraph 
could  have  been  made  to  flow  at  a  uniform  rate  upon  its 
surface,  the  clock  could  now  record  its  beats,  appearing 
as  dots  separated  from  each  other  by  equal  intervals. 
But  it  was  soon  seen  that  the  paper  could  not  be  made  to 
flow  uniformly ;  and  even  had  this  been  possible,  a  single 
night's  work  would  demand  for  its  record  such  a  vast 
amount  of  paper  that  this  method  was  inapplicable  to 
practice.  After  careful  deliberation,  the  "  revolving 
disk"  was  selected  as  the  best  possible  surface  on  which 
the  record  of  time  and  observation  could  be  made.  The 
preference  was  given  to  the  disk  over  the  cylinder  for 
the  following  reasons : — The  uniform  revolution  of  the 
disk  could  be  more  readily  reached.  The  record  on  the 
disk  was  always  under  the  eye  in  every  part  of  it  at  the 
same  time,  while,  on  the  revolving  cylinder,  a  portion  of 
the  work  was  always  invisible.  One  disk  could  be  sub- 
stituted for  another  with  greater  ease,  and  in  a  shorter 
time  ;  and  the  measure  of  the  fractions  of  seconds  could 
be  more  rapidly  and  accurately  performed  on  the  disk 
than  on  the  cylinder. 

After  much  thought  and  experiment  it  was  decided  to 
adopt  "  a  make  circuit''  and  "  a  dotted  scale"  rather  than 


240  INSTRUMENTAL    ASTRONOMY. 

a  "  break  circuit"  and  a  "  linear  scale;"  and  I  think  it 
will  be  seen  hereafter  that  in  this  selection  the  choice  has 
been  fully  justified  in  practice.  These  points  being 
settled,  the  mechanical  problems  now  presented  for  so- 
lution were  the  following  :  First,  To  invent  some  machin- 
ery which  could  give  to  a  disk  of,  say,  twenty  inches 
diameter,  mounted  on  a  vertical  axis,  a  motion  such  that 
it  should  revolve  uniformly  once  in  each  minute  of  time ; 
and,  second,  To  connect  with  this  disk  the  machinery 
which  should  enable  the  clock  to  record  on  the  disk  each 
alternate  second  of  time,  in  the  shape  of  a  delicate  round 
dot.  Third,  The  apparatus  which  should  enable  the  ob- 
server to  record  on  the  same  disk  the  exact  moment  of 
the  transit  of  a  star  across  the  meridian,  or  the  occurrence 
of  any  other  phenomenon. 

The  first  of  these  problems  was  by  far  the  most  diffi- 
cult, and,  indeed,  its  perfect  solution  remains  yet  to  be 
accomplished,  though,  for  any  practical  astronomical  pur- 
pose, the  problem  has  been  solved  in  more  than  one  way. 

The  plan  adopted  in  the  Cincinnati  Observatory  may 
be  described  as  follows  : — The  clock-work  machinery  em- 
ployed to  give  to  the  great  equatorial  telescope  a  uni- 
form motion  equal  to  that  of  the  earth's  rotation,  on  its 
axis,  offered  to  me  the  first  obvious  approximate  solution 
of  the  problem  under  consideration.  This  machinery 
was  accordingly  applied  to  the  motion  of  the  disk,  or 
rather  to  regulate  the  motion  of  revolution,  this  motion 
being  produced  by  a  descending  weight,  after  the  fashion 
of  an  ordinary  clock.  It  was  soon  discovered  that  the 
"  Frauenhofer  clock,"  as  this  machine  is  called,  was  not 
competent  to  produce  a  motion  of  such  uniformity  as  was 
now  required.  Several  modifications  were  made  with  a 
positive  gain ;  but  after  long  study  it  was  finally  dis- 


INSTRUMENTAL  ASTRONOMY.     241 

covered  that  when  the  machinery  was  brought  into  per- 
fect adjustment,  the  dynamical  equilibrium  obtained  was 
an  equilibrium  of  instability  ;  that  is,  if  from  a  motion 
such  as  produced  a  revolution  in  one  exact  minute,  it  be- 
gan to  lose,  this  loss  or  decrement  in  velocity  went  on 
increasing,  or  if  it  commenced  to  gain,  the  increment 
went  on  increasing  at  each  revolution  of  the  disk.  Now 
all  these  delicate  changes  could  be  watched  with  the  most 
perfect  certainty ;  as,  in  case  the  disk  revolved  uniformly 
once  a  minute,  then  the  seconds'  dots  would  fall  in  such 
a  manner  (as  we  shall  see  directly),  that  the  dots  of  the 
same  recorded  seconds  would  radiate  from  the  center  of 
the  disk  in  a  straight  line.  Any  deviation  from  this  line 
would  be  marked  with  the  utmost  delicacy  down  to  the 
thousandth  of  a  second.  By  long  and  careful  study,  it 
was  at  length  discovered,  that  to  make  any  change  in  the 
velocity  of  the  disk,  to  increase  or  decrease  quickly  its 
motion,  in  short,  to  restore  the  dynamical  equilibrium, 
the  winding  key  of  the  "  Frauenhofer  clock"  was  the 
point  of  the  machinery  where  the  extra  helping  force 
should  be  applied;  and  it  was  found  that  a  per- 
son of  ordinary  intelligence,  stationed  at  the  disk,  and 
with  his  fingers  on  this  key,  could,  whenever  he  noticed 
a  slight  deviation  from  uniformity,  at  once,  by  slight  as- 
sistance, restore  the  equilibrium,  when  the  machine  would 
perhaps  continue  its  performance  perfectly  for  several 
minutes,  when  again  some  slight  acceleration  or  retarda 
tion  might  be  required  from  the  sentinel  posted  as  an 
1  auxiliary. 

The  mechanical  problem  now  demanding  solution  was 
very  clearly  announced.  It  was  this  :  Required  to  con- 
struct an  automaton  which  should  take  the  pkce  of  the 
intelligent  sentinel,  watch  the  going  of  the  disk,  and  in- 

11 


242        INSTRUMENTAL     ASTRONOMY. 

stantly  correct  any  acceleration  or  retardation.  This,  in 
fact,  is  the  great  problem  in  all  efforts  to  secure  uniform 
motion  of  rotation.  This  problem  was  resolved  theoreti- 
cally, in  many  ways,  several  of  which  methods  were  exe 
cuted  mechanically  without  success,  as  it  was  found  that 
the  machine  stationed  as  a  sentinel  to  regulate  the  going 
of  the  disk  was  too  weak,  and  was  itself  carried  off  by 
its  too  powerful  antagonist.  The  following  method 
was,  however,  in  the  end,  entirely  successful.  Upon 
the  axis  of  the  winding  key,  already  mentioned,  a 
toothed  wheel  was  attached,  the  gearing  being  so  ad- 
justed that  one  revolution  of  this  wheel  should  pro- 
duce a  whole  number  of  revolutions  of  the  disk.  The 
circumference  of  this  wheel  was  cut  into  a  certain  num- 
ber of  notches,  so  that,  as  it  revolved,  one  of  these  notches 
would  reach  the  highest  point  once  in  two  seconds  of 
time.  By  means  of  an  electro-magnet  a  small  cylin- 
der or  roller,  at  the  extremity  of  a  lever  arm,  was 
made  to  fall  into  the  highest  notch  of  the  toothed 
wheel  at  the  end  of  every  two  seconds.  In  case 
the  disk  was  revolving  exactly  once  a  minute,  the 
roller,  driven  by  the  sidereal  clock,  by  means  of  an 
electro-magnet,  fell  to  the  bottom  of  the  notch,  and 
performed  no  service  whatever ;  but,  in  case  the  disk  be- 
gan to  slacken  its  velocity,  then  the  roller  fell  on  the 
retreating  inclined  face  of  the  notch,  and  thus  urged  for- 
ward by  a  minute  amount  the  laggard  disk,  while,  on  the 
contrary,  should  the  variation  from  a  uniform  velocity 
present  itself  in  an  acceleration,  then  the  roller  struck  on 
the  advancing  face  of  the  notch,  and  thus  tended  slowly 
to  restore  the  equilibrium.  Let  it  be  remembered  that 
this  delicate  regulator  has  but  a  minute  amount  of  service 
to  perform.  It  is  ever  on  guard,  and  detecting,  as  it 


INSTRUMENTAL    ASTRONOMY.  243 

does  instantly,  any  disposition  to  change,  at  once  applies 
its  restoring  power,  and  thus  preserves  an  exceedingly 
near  approach  to  exact  uniformity  of  revolution.  This 
regulator  operates  through  all  the  wheel-work,  and  thus 
accomplishes  a  restoration  by  minute  increments  or  de- 
crements spread  over  many  minutes  of  time. 

With  a  uniformly  revolving  disk,  stationary  in  posi- 
tion, we  should  accomplish  exactly,  and  very  perfectly, 
the  record  of  one  minute  of  time,  presenting  on  the  re- 
cording surface  thirty  dots  at  equal  angular  intervals  on 
the  circumference  of  a  circle.  To  receive  the  time  dots 
of  the  next  minute  on  a  circle  of  larger  diameter,  re- 
quired either  that  the  recording  pen  should  change  posi- 
tion, or  that  at  the  end  of  each  revolution  the  disk  itself 
should  move  away  from  the  pen  by  a  small  amount.  We 
chose  to  remove  the  disk.  To  accomplish  accurately  the 
change  of  position  of  the  disk,  at  the  end  of  each  revolu- 
tion, the  entire  machine  was  mounted  on  wheels  on  a 
small  railway  track,  and  by  a  very  delicate  mechanical 
arrangement  accomplished  its  own  change  of  position 
between  the  fifty-ninth  and  sixtieth  second  of  every 
minute. 

THE  RECORDING  PENS. — It  now  remains  only  to  de- 
scribe the  simple  machinery  by  which  the  clock  records 
its  beats,  and  the  observer  makes  the  record  of  his  obser- 
vation. These  instruments  are  called  the  recording  pens. 
That  belonging  to  the  clock  is  called  the  time  pen ;  the 
one  used  by  the  observer  the  observing  pen.  They 
are  constructed  and  operate  in  the  following  man- 
ner :  A  metallic  arm  is  constructed  with  a  short  axis, 
perpendicular  to  its  length.  The  extremities  of  this  axis 
are  pivots  working  in  the  jaws  of  a  metallic  frame,  which 
supports  the  axis  of  the  pen  in  a  horizontal  position.  The 


244         INSTRUMENTAL     ASTRONOMY. 

longer  arm  of  the  pen  reaches  over  into  the  center  of  the 
disk,  and  is  armed  at  its  extremity  with  a  steel  point  or 
stylus.  Upon  the  long  arm  of  the  pen  and  near  the  axis 
is  located  a  piece  of  soft  iron  denominated  an  armature, 
and  beneath  this  armature  an  electro-magnet  is  firmly 
fixed.  This  magnet  is  placed  on  the  circuit  closed  by  the 
wire-cross  vibrating  with  the  clock  pendulum,  and  thus, 
at  every  dip  of  the  cross  into  the  mercury  cup,  the  arma- 
ture of  the  pen  is  suddenly  drawn  down  on  the  head  of 
the  magnet,  and  the  moment  the  circuit  is  broken  a 
spring  acting  on  the  short  arm  of  the  pen  lifts  it  from 
the  head  of  the  magnet.  It  is  readily  seen  that  in  this 
way  the  stylus  is  brought  down  by  a  sudden  shock  or 
blow  on  the  material  placed  on  the  revolving  disk  to  re- 
ceive the  record.  The  pen  is  so  adjusted  that  in  case 
the  armature  be  simply  placed  and  held  by  hand  on  the 
head  of  the  magnet,  the  steel  point  of  the  stylus  does  not 
quite  touch  the  recording  surface  on  the  disk.  The  elas- 
ticity of  the  long  arm  of  the  pen  is,  therefore,  a  matter  of 
the  greatest  moment,  for  this  elasticity  causes  the  pen 
to  make  a  simple  dot,  by  a  sudden  blow  and  recoil ; 
whereas  were  the  pen  non-elastic,  there  would  be  a  drag 
for  the  time  during  which  the  magnet  holds  the  pen, 
which  would  at  once  destroy  the  uniformity  in  the  going 
of  the  disk. 

A  pen  constructed  in  precisely  the  same  way,  and 
placed  at  right  angles  to  the  former,  so  that  the  points  of 
the  two  pens  fall  in  close  proximity  on  the  disk,  is  oper- 
ated by  a  magnet  made  by  a  circuit  closed  at  will  by  the 
finger  of  the  observer  ;  and  thus  he  is  enabled  to  throw 
down  upon  the  time  scale  a  dot,  which,  falling  between 
some  two-second  dots  on  the  disk,  records  the  exact  in- 
stant of  any  phenomenon  under  observation. 


INSTRUMENTAL    ASTRONOMY.  245 

When  the  disk  is  filled,  we  have  only  to  lift  it  from  its 
socket  and  replace  it  with  a  new  disk.  To  read  the  time 
scale  it  is  only  necessary  to  mark  on  the  disk  from  the  clock 
face  the  time  denoted  by  any  one  dot ;  for  example,  12h. 
15m.  OOs.  The  circle  next  outside  will  be  12h.  16m.,  the 
next  circle  12h.  17m.,  &c. ;  while  the  first  or  marked  radius 
of  dots  will  be  the  0  second  of  all  the  minutes,  the  next 
in  order  will  be  the  second,  the  next  the  fourth,  and  so 
on  to  the  58th  and  0  second  again.  Thus  we  read  the 
scale  as  rapidly  as  we  read  a  clock  face,  for  the  hour,  min- 
ute and  second ;  and  it  only  remains  to  construct  a  ma- 
chine for  measuring  the  fractions  of  seconds. 

THE  ANGULAR  TIME  MICROMETER. — This  instrument 
is  very  simple.  Take  a  common  carpenter's  two-foot 
rule  ;  cut  away  the  inner  portion  of  one  of  the  legs  for 
two-thirds  of  its  length,  and  insert  a  piece  of  plane  glass ; 
draw  from  the  centre  of  the  joint  with  a  diamond  point, 
on  the  under  surface  of  this  glass,  a  delicate  straight  line, 
and  blacken  by  rubbing  in  black  lead  pencil.  The  arms 
of  this  micrometer  are  a  little  longer  than  the  radius  of 
the  disk.  To  the  left  hand  arm,  at  its  outer  extremity, 
attach  a  small  brass  arc,  divided  into  seconds  and  tenths, 
and  make  it,  say,  2^  seconds  in  length.  When  the  two 
legs  are  closed  the  black  line  on  the  glass  will  read  0  on 
this  scale  of  seconds.  At  the  joint  drill  a  small  hole,  and 
at  the  center  of  the  disk  to  be  measured  erect  a  small 
vertical  pin  to  fit  this  hole.  Lay  the  instrument  on  the 
disk,  the  pin  being  inserted  in  the  hole,  and  thus  the 
fractions  of  seconds  may  be  measured  with  any  degree  of 
precision. 

Such  is  an  outline  of  the  machinery  now  in  use  in  the 
Dudley  Observatory  at  Albany,  and  at  the  Cincinnati 
Observatory. 


246  INSTRUMENTAL    ASTEONOMY. 

As  we  have  seen,  in  the  old  method  of  transits  the  at- 
tention of  the  observer  was  divided  among  many  objects. 
He  was  compelled  to  keep  up  the  counting  of  the  clock 
beat ;  to  estimate  the  space  passed  over  by  the  star  under 
observation  in  a  second  of  time  ;  to  subdivide  this  space 
by  estimation  into  tenths;  to  write  down  in  his  note- 
book the  observed  moment  of  transit  across  each  of  the 
wires,  and  all  this  while  his  eye  continued  to  follow  the 
iLovement  of  the  object  under  observation.  To  give  the 
observer  time  to  make  his  record,  the  spider's  lines  or 
wires  were  necessarily  separated  by  such  an  interval 
from  each  other  that  several  seconds  would  be  required 
by  the  star  to  pass  from  one  to  the  other,  and  thus  but 
few  wires  could  be  employed  in  transit  observations. 

In  the  new  method  the  observer  is  released  from  all 
responsibility  with  reference  to  time,  counting  of  clock 
beat,  estimation  of  spaces,  or  entries  in  note-book.  The 
clock  records  its  own  beat,  and  the  observer  has  nothing 
to  do  but  touch  a  magnetic  key  at  the  exact  moment  in 
which  his  star  is  bisected  by  the  meridian  wire.  This 
touch  records  the  moment  of  observed  transit,  and  as  this 
record  is  accomplished  almost  instantaneously,  the  ob- 
server is  ready  to  record  the  transit  across  the  next  wire, 
and  thus  the  interval  between  the  wires  may  be  greatly 
reduced,  and  their  number  extended  almost  indefinitely. 
While  in  the  old  method  long  practice  was  required  to 
make  an  accomplished  observer  (the  best  of  whom  could 
not  record  more  than  the  transits  on  seven  wires),  in  the 
new  method  a  few  nights  of  practice  gives  all  desirable 
experience,  and  the  observer  may  record  the  transits 
across  as  many  as  fifty  wires,  should  so  large  a  number 
ever  be  desirable  under  any  circumstances.  It  is  found 
in  the  use  of  this  method  that  erroneous  habits  of  obser- 


INSTRUMENTAL    ASTRONOMY.  247 

vation  may  either  be  entirely  avoided  or  detected,  and 
thus  corrected.  It  furnishes  the  means  of  measuring 
with  great  accuracy,  the  value  of  personal  equation,  and 
has  demonstrated,  indeed,  that  the  large  differences  exist- 
ing between  observers,  amounting  in  some  instances  to  a 
whole  second  of  time,  are  not  due  to  physiological  consti- 
tution, but  almost  entirely  to  false  habits  of  observation 
It  has  furnished  the  means  of  measuring  the  amount  of 
time  which  elapses  between  the  occurrence  of  any  phe- 
nomenon falling  within  the  grasp  of  the  senses  of  sight 
and  hearing,  and  the  possible  record  by  the  touch  of  a 
magnetic  key.  In  this  operation  there  are  three  distinct 
processes,  the  sense  of  sight,  for  example,  conveys  to  the 
brain  information  of  the  occurrence  of  the  external  phe- 
nomenon ;  the  mind  thus  perceives,  and  the  will  issues  an 
order  to  the  nerves  to  record ;  the  nerves  execute  this 
order.  Thus  far  it  has  been  impossible  to  ascertain  the 
amount  of  time  occupied  in  each  of  these  processes,  but 
the  sum  of  the  times,  or  that  elapsing  between  the  mo- 
ment of  occurrence  of  a  phenomenon  and  its  record,  has 
been  measured  both  for  the  sense  of  sight  and  the  sense 
of  hearing,  in  a  large  number  of  persons  of  both  sexes 
and  of  all  ages.  From  these  experiments  it  has  been  as- 
certained that  while  different  individuals  present  promi- 
nent and  marked  differences,  these  differences  are  only 
found  to  exist  in  the  hundredths  of  a  second  of  time,  and 
not,  as  has  been  imagined,  in  whole  seconds.  In  con- 
ducting these  experiments  it  was  ascertained  that  all  ob- 
servers, without  a  single  exception,  in  attempting  to 
mark  the  moment  at  which  a  star  crossed  a  wire,  antici- 
pated the  moment  of  transit,  and  the  recorded  time  was 
thus  in  advance  of  the  true  time.  Having  learned  this 
feet,  the  observer  is  placed  upon  his  guard,  and  is  fur- 


248  INSTRUMENTAL    ASTRONOMY. 

nished  with  the  means  of  correcting  this  false  habit,  and 
of  bringing  himself  up  to  a  standard  of  positive  accuracy. 
Another  advantage  derived  from  this  mode  of  observation 
arises  from  the  fact  that  it  imposes  but  a  blight  tax  upon 
the  nervous  system,  and  hence  an  observer  is  able  to 
continue  his  work  without  exhaustion  for  a  much  longer 
period  of  time. 

We  have  mentioned  that  one  of  the  most  hidden 
sources  of  error  lies  in  the  uncertainty  of  the  rate  of 
going  of  the  clock.  The  old  methods  furnish  the  means 
of  ascertaining  with  comparative  accuracy  how  much  the 
clock  has  lost  or  gained  in  twenty-four  hours ;  and  if  this 
quantity  should  amount  only  to  a  fraction  of  a  second, 
it  is  almost  impossible  to  assert  that  this  loss  or  gain 
may  not  have  occurred  even  a  hundred  times,  or  pos- 
sibly a  thousand  times  during  the  twenty-four  hours. 
By  causing  two  or  more  clocks  to  record  their  beats 
upon  the  same  time-scale,  the  new  method  furnishes  the 
jaeans  of  inter-comparison  between  these  clocks,  even 
from  second  to  second,  if  required,  and  thus  from  a 
record  of  this  kind  may  be  obtained  a  positive  standard 
of  time. 

The  electro-magnetic  method  of  observation  in  connec- 
tion with  the  system  of  telegraphic  wires,  now  extended 
over  nearly  all  the  civilized  world,  furnishes  a  very  rapid 
and  exact  method  of  determining  the  difference  of  longi- 
tude between  any  two  points.  This  difference  of  longi- 
tude is  nothing  more  than  the  time  which  elapses  from 
the  transit  of  a  star  across  the  meridian  of  one  place  until 
it  crosses  the  meridian  of  the  other  place.  In  case  the 
two  observatories  whose  difference  of  longitude  is  required 
are  connected  by  telegraph,  and  are  furnished  with  the 
electro-magnetic  apparatus,  the  observer  in  the  eastern 


INSTRUMENTAL    ASTRONOMY.  249 

observatory  may  send  to  his  correspondent  by  telegraph 
the  moment  of  transit  of  the  star  across  his  own  meridian. 
He  will  receive  in  return  by  telegraph  the  moment  the 
same  star  crosses  the  meridian  of  the  western  observatory, 
and  in  case  the  observations  are  perfectly  made,  transmit- 
ted with  infinite  velocity  along  the  wires,  and  recorded 
with  perfect  accuracy,  the  result  will  be  absolutely  per- 
fect. The  common  errors  of  observation  are  readily  elimin- 
ated, the  errors  of  recording,  in  like  manner,  are  easily 
detected  and  measured,  and  the  only  matter  of  difficulty 
which  remains  is  to  ascertain  whether  the  message  sent 
along  the  wire  travels  at  a  finite  rate,  and  if  so,  to  deter- 
mine what  this  rate  may  be.  The  conversion  of  time 
into  space,  and  the  delicacy  of  the  machinery  now  em- 
ployed in  recording  and  subdividing  time,  has  furnished 
the  means  of  measuring  the  velocity  with  which  signals 
are  transmitted  along  the  wires  of  the  telegraph.  No 
doubt  this  velocity  is  modified  by  a  variety  of  circum- 
stances, and  may  depend  upon  the  direction  in  which  the 
telegraphic  wire  is  laid,  the  season  of  the  year,  the  tem- 
perature of  the  earth  and  atmosphere,  but  none  of  these 
causes  can  interfere  to  mar  the  accuracy  of  the  work  em- 
ployed for  longitude  purposes ;  for  there  is  no  difficulty  in 
determining  the  exact  velocity  with  which  the  signals  are 
transmitted  by  the  wires  at  the  time  of  observation. 
These  are  a  few  among  many  advantages  which  have  been 
gained  by  the  conversion  of  time  into  space,  and  the  ap- 
plication of  this  principle  to  the  observation  of  astrono- 
mical transits. 

The  author  has  attempted  to  add  something  to  the 
facility  and  accuracy  of  the  determination  of  north  polar 
distanceSj  the  second  great  element  employed  in  fixing 
the  place  of  a  heavenly  body.  As  already  explained, 


250  INSTRUMENTAL    ASTRONOMY. 

this  element  is  reached  by  the  division  of  a  circle  attached 
to  the  axis  of  the  transit,  and  the  accuracy  of  the  work 
depends  upon  the  perfection  of  these  divisions,  the  per- 
manence of  the  figure  of  the  circle,  the  permanence  in 
the  place  of  the  reading  microscopes,  and  the  precision 
attainable  in  reading  the  subdivisions  of  the  circle.  As 
the  errors  which  arise  from  these  different  sources  are 
found  to  be  comparatively  large,  for  the  measurement  of 
small  differences  of  north  polar  distances,  or  small  arcs 
of  space,  resort  has  been  had  to  other  and  more  delicate 
mechanical  contrivances,  hence  the  invention  and  con- 
struction of  the  various  micrometers  now  in  use,  all  of 
which  depend  for  their  accuracy  upon  the  performance 
of  a  micrometer  screw.  Very  extended  experiments  with 
these  instruments  first  created  a  doubt  in  my  own  mind 
as  to  the  accuracy  with  which  the  micrometer  screw 
would  repeat  its  own  measures.  This  doubt,  added  to  the 
fact  that  the  measurements  by  the  micrometer  were  very 
slow  and  tedious,  gave  rise  to  the  effort  which  has  resulted 
in  the  construction  of  a  new  system  whereby  differences 
of  north  polar  distance  may  be  determined  with  great 
rapidity  and  precision,  which  principle  can  readily  be  ex- 
tended to  the  determination  of  absolute  north  polar  dis- 
tances. A  description  of  the  machinery  employed  for 
this  purpose  may  be  found  elsewhere.  We  are  only 
concerned  here  to  notice  some  of  the  possible  advan- 
tages of  this  new  method  of  north  polar  distances.  I 
will  only  state  that  the  machinery  employed  in  all  its 
joints  and  connections  is  of  the  simplest  kind,  and  every- 
where visible  to  the  eye.  There  is  no  concealed  portion, 
as  in  the  screw  micrometer,  no  joints  to  grow  imperfect 
by  wearing,  and  no  strong  resistance  to  change  the  figure 
of  any  part  of  the  machinery.  If  the  tube  if  the  tele- 


INSTRUMENTAL    ASTRONOMY.  251 

scope,  loaded  as  it  is  with  the  weight  of  the  object  glass 
and  eye-piece,  and  its  own  weight,  can  be  depended  upon 
to  retain  its  figure  without  a  counterpoise,  it  is  absolutely 
certain  that  the  declination  arm,  which  in  the  new  method 
is  attached  to  the  axis  of  the  transit,  if  perfectly  counter- 
poised and  bearing  no  weight  whatever,  can  be  relied  upon 
to  retain  its  figure.  The  lower  extremity  of  this  arm, 
moving  .as  it  does  in  north  polar  distance,  with  the  line 
of  collimation  of  the  telescope,  by  a  connecting  bar,  gives 
motion  to  the  axis  of  the  reading  microscope,  which, 
being  directed  to  a  distant  scale,  magnifies  in  a  very  high 
ratio  by  mechanical  means  the  arc  through  which  the 
transit  revolves  in  the  plane  of  the  meridian.  Thus  it 
will  be  seen  that  this  new  method  is  nothing  more  than 
the  use  of  a  mechanical  magnifier ,  and  the  only  question 
is,  can  the  scale  be  so  divided  as  to  read  seconds  of  arc, 
and  can  it  be  made  of  invariable  length?  There  is 
little  difficulty  in  accomplishing  both  of  these  objects, 
for  scales  have  already  been  divided  with  such  precision 
that  no  error  amounting  to  the  hundredth  part  of  a  single 
second  of  arc  could  possibly  exist ;  and  in  order  to  re- 
tain an  invariable  length  in  the  scale  all  that  is  necessary 
is  to  grade  it  upon  a  surface  constituting  one  face  of  a 
rectangular  tube ;  fill  this  tube  with  water  and  broken 
ice,  and  thus  a  permanent  temperature  of  32°  may 
be  had  for  any  length  of  time.  To  measure  the  exact 
value  of  the  divisions  on  the  scale  we  have  only  to  em- 
ploy these  divisions  in  measuring  around  the  entire  cir- 
cumference of  the  circle  attached  to  the  axis  of  the  tran- 
sit. Suppose  the  length  of  the  scale  to  be  sixty  minutes 
approximately,  then  if  this  length  is  contained  360  tunes 
in  the  whole  circumference,  its  approximate  value  be- 
comes its  absolute  value,  and  at  all  events  this  experiment 


252  INSTRUMENTAL    ASTRONOMT. 

furnishes  the  means  of  determining  the  absolute  value. 
Thus  while  the  circle  furnishes  the  means  of  measuring 
the  scale,  the  scale  furnishes  in  return  the  means  of 
measuring  the  subdivisions  of  the  circle.  These  amount 
only  to  360,  and  may  be  reduced  even  to  the  fifth  part 
of  this  number,  should  practice  prove  this  reduction  de- 
sirable. This  small  number  of  divisions  can  rapidly  be 
read  up  with  a  scale  of  invariable  length,  and  .by  per- 
forming this  reading  at  temperatures  widely  different  a 
correction  for  temperature  may  be  determined  with  great 
exactness.  In  the  old  circle,  as  there  are  no  less  than 
ten  thousand  divisions,  and  as  there  exists  no  permanent 
scale  for  the  reading  of  these  divisions,  it  becomes  almost 
impossible  to  learn  their  actual  values  and  to  tabulate 
their  errors,  hence  astronomers  have  been  compelled  to 
rely  to  a  great  extent  upon  the  assumed  accuracy  of  the 
subdivisions  of  their  circles,  as  received  from  the  hands  of 
the  manufacturer. 

By  a  combination  of  the  electro-magnetic  method,  with 
the  new  method  of  measuring  north  polar  distances,  a  very 
simple,  convenient,  and  accurate  instrument  is  obtained 
for  recording  the  places  of  the  stars  or  other  heavenly 
bodies  with  great  rapidity  and  exactitude,  rendering  it 
possible  to  construct,  in  a  comparatively  short  time,  a 
very  extended  and  exact  catalogue  of  the  places  of  all  the 
fixed  stars,  clearly  visible,  with  any  optical  power. 

We  have  thus  presented  a  rapid  sketch  of  the  old  and 
new  methods  of  fixing  the  elements  for  the  determination 
of  the  heavenly  bodies,  it  only  remains  in  this  connec- 
tion to  speak  of  the  optical  power  of  the  telescope. 

These  instruments  are  divided  into  two  great  classes, 
called  reflecting  and  refracting  telescopes.  In  the  re- 
flecting telescopes  the  rays  of  light  from  the  external  ob? 


INSTEUMENTAL    ASTRONOMY.  253 

ject,  passing  down  the  tube  of  the  telescope,  fall  upon  a 
metallic  mirror  or  speculum,  whose  surface,  perfectly 
polished,  has  the  figure  of  a  paraboloid  of  revolution, 
Being  reflected  by  this  surface,  the  rays  of  light  are  con- 
centrated at  a  certain  point,  called  the  focus,  where  an 
intensely  luminous  image  of  the  object  is  formed.  This 
image  is  then  examined  by  a  magnifying  glass  or  eye- 
piece, and  its  dimensions  expanded  to  any  required  de- 
gree. 

In  the  refracting  telescope  the  light  falls  upon  what 
is  called  the  object-glass^  a  powerful  lens,  which  con- 
centrates, by  refraction,  the  rays  of  light  which  pass 
through  it,  thus  forming  an  image  of  the  object  at  the 
focal  point.  This  image  is  then  examined,  as  in  the  re- 
flecting telescope,  by  eye-pieces  having  different  magni- 
fying powers.  Hitherto  it  has  been  found  impracticable 
to  construct  object-glasses  of  any  very  considerable  dia- 
meter, the  largest  of  these  glasses  in  use  not  exceeding 
sixteen  to  twenty  inches  in  diameter.  These  narrow 
limits  do  not  exist,  however,  in  the  construction  of  the 
metallic  specula  which  belong  to  the  reflecting  telescope  ; 
and  hence  we  find  gigantic  instruments  have  been  con- 
structed by  different  observers,  one  of  which,  now  in  use 
by  Lord  Ross,  has  a  speculum  of  no  less  than  six  feet  in 
diameter,  with  a  focal  length  of  fifty-two  feet.  Such 
immense  instruments,  requiring  ponderous  machinery  for 
their  management,  are  not  well  adapted  for  that  kind  of 
observation  having  for  its  object  to  determine  the  places 
of  the  heavenly  bodies.  Their  use  has  been  rather  con- 
fined to  examinations  of  the  planets,  double  stars,  clus- 
ters, and  nebulae,  demanding  a  large  amount  of  light 
rather  than  a  perfect  definition  or  exactitude  in  measure- 
ment. It  is  true,  that  in  the  hands  of  Lassell,  of  Liver- 


254  INSTRUMENTAL    ASTRONOMY. 

pool,  we  find  the  reflecting  telescope  performing  admir- 
ably in  the  routine  work  of  an  observatory.  But  these 
instruments  are  comparatively  small,  their  dimensions 
not  much  exceeding  those  of  the  largest  refractors. 

There  are  two  qualities  which  distinguish  the  telescope, 
the  space-penetrating  power  and  the  power  of  definition. 
The  first  of  these  depends  exclusively  upon  the  amount 
of  light  received  and  refracted,  or  reflected  to  the  focus, 
and  thus  forming  the  image.  In  case  all  the  light  fall- 
ing upon  the  object-glass  or  speculum  could  be  concen- 
trated in  the  formation  of  the  image,  then  the  space-pene- 
trating power  of  telescopes  would  be  exactly  proportioned 
to  the  diameters  of  their  apertures,  and  we  can  compare 
then,  readily,  the  space-penetrating  power  of  different 
instruments,  not  only  among  themselves?,  but  directly 
with  the  space-penetrating  power  of  the  human  eye.  The 
diameter  of  the  pupil  of  the  eye  determines  the  amount 
of  light  which  can  enter  and  form  the  image,  just  as  the 
diameter  of  an  object-glass  in  a  telescope  determines  the 
amount  of  light  which  in  that  instrument  forms  the  focal 
image;  hence,  if  we  desire  to  know  how  many  times 
deeper  a  telescope  can  penetrate  space  than  the  eye,  we 
have  only  to  learn  how  many  times  the  area  of  the  ob- 
ject-glass exceeds  that  of  the  pupil  of  the  eye.  We  shall 
have  occasion  hereafter  to  employ  this  principle  when  we 
come  to  examine  the  relative  distances  to  which  the  ne- 
bulae and  clusters  are  sunk  in  space. 

We  have  only  spoken  of  the  mounting  of  the  transit^ 
with  its  attached  circle,  for  reading  north  polar  distances. 
This  instrument  revolves  only,  as  we  have  seen,  in  the 
plane  of  the  meridian,  and  of  course  no  object  can  be 
seen  with  the  transit  except  when  in  the  act  of  passing 
the  meridian  line. 


INSTRUMENTAL     ASTRONOMY.         255 

A  telescope  mounted  in  such  a  manner  that  it  can  be 
directed  to  any  point  of  the  heavens,  is  called  an  extra- 
meridional  instrument,  and  of  these  the  equatorial  is 
the  most  used,  and  is  the  best  adapted  for  all  observations 
off  the  meridian.  The  tube  of  the  telescope  is  carried  by 
a  heavy  metallic  casting,  very  firm  and  strong,  which  is 
made  fast  to  a  metallic  cylinder,  through  which  passes  a 
steel  axis,  called  the  equatorial  axis.  The  metallic  cylin- 
der is  also  screw-bolted  tc  the  extremity  of  a  heavy  steel 
axis,  so  placed  on  its  supports  as  to  lie  parallel  to  the 
earth's  axis.  These  supports  rest  on  heavy  metallic 
plates,  bolted  to  a  massive  stone  pier,  called  the  "foot 
of  the  instrument,"  which,  in  turn,  is  placed  on  the  top 
of  a  heavy  pier  of  masonry,  resting  on  a  rock  foundation, 
or  something  equally  solid,  and  entirely  disconnected 
from  the  building. 

The  instrument  is  so  counterpoised  in  all  its  many 
parts  as  to  be  readily  moved  either  on  its  polar  or  equa- 
torial axis,  and  may  thus  be  directed  to  any  point  of  the 
celestial  sphere.  To  enable  the  observer  to  follow  the 
object  under  examination  these  telescopes  are  usually  fur- 
nished with  a  species  of  clock-work,  which  causes  the 
instrument  to  revolve  round  its  polar  axis  with  a  velocity 
equal  to  that  of  the  earth's  rotation,  causing  it  to  follow 
a  heavenly  body  and  to  hold  it  steady  in  the  field  of  view 
for  any  required  period  of  time. 

Without  extending  further  our  notice  of  the  instru- 
ments employed  in  reaching  the  data  required  in  astrono- 
mical investigation,  we  will  now  return  to  our  examination 
of  the  bodies  which  compose  the  sun's  retinue,  and  shall 
proceed  in  our  plan,  preserving  the  order  of  distance 
from  the  sun. 

The  interruption  which  was  made  after  closing  the 


256         INSTRUMENTAL     ASTRONOMY. 

discussion  of  the  system  of  Saturn,  to  introduce  to  the 
student  the  laws  of  motion  and  gravitation,  and  the  in- 
struments employed  in  astronomical  measures,  was  neces- 
sary to  a  full  comprehension  of  the  extraordinary  inves- 
tigations which  are  now  to  follow.  We  are  hereafter  to 
treat  the  planets  and  their  satellites  as  ponderable  hodies, 
mutually  affecting  each  other,  and  all  subjected  to  the 
dominion  of  the  laws  of  motion  and  gravitation. 


CHAPTER   XII. 

URANUS,    THE  EIGHTH   PLANET  IN  THE  ORDER  OP  THE 
DISTANCE  FROM  THE  SUN. 

ACCIDENTALLY  DISCOVERED  BY  SIB  WILLIAM  HEKSCHELL.— ANNOUNCED  AS  A 
COMET.— ITS  ORBIT  PBOVED  IT  TO  BE  A  SUPERIOR  PLANET.— THE  ELEMENTS 
or  ITS  ORBIT  OBTAINED. — ABC  OF  RETROORADATIOX. — PERIOD  or  REVOLU- 
TION.— FIGURE  or  THE  PLANET. — INCLINATION  or  ITS  ORBIT. — Six  SATEL- 
LITES ANNOUNCED  BY  THE  ELDER  HEBSCHELL.— FOUR  or  THESE  NOW 
RECOGNIZED.— THEIR  ORBITAL  PLANES  AND  BISECTIONS  or  REVOLUTION 
ANOMALOUS. — EFFORTS  MADE  TO  TABULATE  THE  PLACES  or  UBANUS  UNSUC- 
CESSFUL.— THIS  LEADS  TO  THE  DISCOVERY  or  A  NEW  EXTERIOR  PLANET. 

IT  was  remarked  at  the  close  of  our  investigation  of  the 
Saturnian  system  that  this  planet  inclosed  by  its  orbit 
all  the  objects  belonging  to  the  solar  system  which  were 
known  to  the  ancients,  and  whose  phenomena,  as  observed 
and  recorded  in  all  time,  furnished  the  data  for  the  dis- 
covery of  Kepler's  laws  and  the  law  of  universal  gravi- 
tation, as  finally  revealed  by  Newton.  While  many  of 
the  modern  astronomers,  from  an  examination  of  the 
inter-planetary  spaces,  had  ventured  to  suggest  the  pro- 
bable existence  of  a  large  planet  revolving  in  an  orbit 
intermediate  between  those  of  Mars  and  Jupiter,  no 
one  had  ventured  to  predict  the  possible  discovery  of 
planets  lying  exterior  to  the  mighty  orbit  of  Saturn. 
From  the  very  dawn  of  astronomy  this  planet  had 
held  the  position  of  sentinel  on  the  outposts  of  the 
planetary  system,  and  many  strong  minds  had  long  en- 


258  URANUS. 

tertained  the  opinion  that  no  other  bodies  existed  exterior 
to  the  orbit  of  Saturn  forming  a  part  of  the  scheme  of 
worlds  revolving  around  the  sun.  Such,  indeed,  was  the 
prevalence  of  this  opinion  that  when,  in  1781,  Sir  William 
Herschell,  in  a  course  of  systematic  exploration  of  the 
heavens,  discovered  an  object  having  a  well-defined  plan- 
etary disk,  and  whose  movement  among  the  fixed  stars 
became  measurable,  even  at  the  end  of  a  few  hours,  he 
did  not  even  suspect  this  new  object  to  be  a  planet,  but 
announced  to  the  world  that  he  had  discovered  a  most 
extraordinary  comet,  without  any  of  the  usual  haziness 
which  attends  these  bodies,  but  presenting  a  clear  and 
well  defined  planetary  disk. 

This  newly-discovered  object  soon  attracted  universal 
attention.  It  was  observed  at  the  royal  observatory  at 
Greenwich,  and  the  then  astronomer  royal,  Dr.  Marke- 
lyne,  was  the  first  to  suspect  its  planetary  character. 
Efforts  were  made  by  several  computers  to  give  to  the 
new  comet,  as  it  was  called,  a  parabolic  orbit ;  this,  how- 
ever, was  found  to  be  impossible,  and  it  was  very  soon 
found  that  the  newly-discovered  object  was  revolving 
around  the  sun  in  an  orbit  nearly  circular  in  form,  lying 
in  a  plane,  nearly  coincident  with  the  ecliptic,  and  com- 
pleting its  mighty  revolution  in  a  period  of  no  less  than 
eighty-two  years.  It  must  be  remembered  that  these 
extraordinary  discoveries  and  announcements  were  made 
at  the  end  of  a  very  short  examination,  while  the 
periods  of  revolution  of  all  the  old  planets  had  been 
obtained  from  actual  observation,  through  long  centuries 
of  patient  watching.  The  periodic  time  of  this  last  dis- 
covered of  all  the  planets,  which,  by  the  old  method  of 
watching  its  return  to  the  same  fixed  star,  could  not  have 
been  determined  in  less  than  eighty-two  years,  and  even 


URANUS.  259 

then  only  approximately,  was,  by  the  new  method,  based 
upon  the  law  of  universal  gravitation,  guided  by  the  re- 
sults of  a  few  nights  of  accurate  observation,  and  worked 
out  by  the  powerful  formulae  of  analytic  reasoning, 
given  to  the  world  with  accuracy  after  only  a  few 
months  of  investigation.  This  is  the  first  illustration 
of  the  change  wrought  in  the  whole  movement  of  astron 
omical  science  by  the  great  discoveries  of  Newton,  and 
by  the  almost  equally  extraordinary  step  accomplished 
by  Descartes,  in  fastening  the  powers  of  analysis  upon 
geometry.  All  the  circumstances  of  motion  of  this  planet 
were  rapidly  investigated ;  the  eccentricity  of  its  orbit ; 
the  position  of  its  perihelion  ;  the  inclination  of  its  orbit 
to  the  plane  of  the  ecliptic ;  the  position  of  its  line  of 
nodes ;  the  measure  of  its  actual  diameter ;  the  determ- 
ination of  its  various  distances  from  the  sun,  all  these 
and  many  other  peculiarities  were  accurately  determined 
from  actual  observation  and  computation.  These  facts 
strike  us  with  the  more  astonishment  when  we  reflect  that 
the  planet  Uranus  is  removed  to  a  distance  of  eighteen  hun- 
dred ml/lions  of  miles  from  the  sun,  and  that,  although 
its  actual  diameter  is  thirty-Jive  thousand  miles,  it  is  ab- 
solutely invisible  to  the  naked  eyed,  and,  when  seen 
through  the  most  powerful  telescope,  presents  a  disk  of 
only  the  five  hundredth  part  of  the  apparent  diameter  of 
the  sun.  At  such  an  immense  distance  it  has  been  im- 
possible thus  far  to  determine  anything  with  reference 
to  the  precise  figure  of  Uranus.  The  discoverer  of  the 
planet  thought  that  he  saw  a  flattening  at  the  poles,  but 
subsequent  observation  has  not  confirmed  this  announce- 
ment. We  have  only,  therefore,  analogy  to  induce  us 
to  believe  that  this  planet,  like  all  the  others,  rotates 
upon  an  axis,  and  that,  consequently,  its  figure  is  that 


260  URANUS. 

of  the  ellipsoid  and  not  of  the  sphere.  The  immense  mag- 
nitude of  the  orbit  of  Uranus,  when  compared  with  that 
of  the  earth,  causes  this  planet  to  retrograde  over  an  arc 
of  only  3°  36',  but  the  duration  of  the  retrograde  motion 
extends  over  a  period  of  no  less  than  one  hundred  and 
fifty-one  days.  No  telescope  has  yet  been  able  to  discern, 
upon  the  surface  of  Uranus,  any  spot  or  belt,  or  any  well- 
defined  point,  distinguished  from  the  entire  surface,  so 
that  we  have  no  means,  thus  far,  of  fixing  the  period  of 
rotation  upon  its  axis.  The  amount  of  light  and  heat 
received  by  Uranus,  admitting  the  law  of  diminution, 
which  seems  to  govern  these  elements,  could  only  be  the 
quarter  part  of  that  received  by  the  planet  Saturn,  while 
the  apparent  diameter  of  the  sun,  as  sden  from  Uranus, 
would  be  less  than  the  thirtieth  part  of  his  diameter,  as 
seen  from  the  earth. 

This  planet  is  surrounded  by  at  least  four  satellites. 
Two  others  were  announced  by  Sir  Wm.  Herschel,  who 
not  only  gave  their  distances  but  their  periods  of  revolu- 
tion, yet  no  telescope  has  since  been  able  to  detect  these 
minute  points  of  light,  and  their  very  existence  is  now 
doubted  by  many  of  the  best  observers.  Four  of  the 
satellites  had  been  studied,  with  much  care,  and  their 
periods  of  revolution  and  their  mean  distances  had  been 
well  determined.  Of  these,  the  second  and  fourth  are 
most  readily  seen,  and  different  astronomers  have  obtained 
results  which  agree  with  each  other  within  comparatively 
small  limits  of  error.  Thus,  the  elder  Herschel  fixed 
the  period  of  revolution  of  the  second  satellite,  in  the  order 
of  distance,  at  8d.  16h.  56m.  5s.  Sir  John  Herschel 
made  the  same  period  twenty-six  seconds  longer.  Dr. 
Lament,  of  Munich,  obtained,  for  this  same  period, 
a  value  of  8d.  16h.  56m.  28s.5.  The  period  of  revolu- 


URANUS.  261 

tion  of  the  fourth  satellite,  in  the  order  of  distance,  as  de- 
termined by  Lament,  amounts  to  13d.  llh.  07m.  06s.3. 
The  period  of  revolution  of  the  nearest  satellite  is  about 
five  days  and  twenty-one  hours,  while  the  third  satellite 
in  order  of  distance  performs  its  revolution  in  a  period  of 
about  eleven  days.  These  are  among  the  most  difficult 
of  all  the  objects  revealed  to  the  eye  by  telescopic  power. 
After  Sir  Wm.  Herschell  no  one  for  many  years  was 
able  to  see  any  of  these  satellites,  the  forty-foot  reflector 
of  Herschel  having  gone  into  disuse.  In  1828,  Sir  John 
Herschel,  after  many  unsuccessful  attempts,  by  confin- 
ing himself  in  a  dark  room  for  many  minutes  previous  to 
observation,  and  thus  giving  to  the  eye  great  acuteness, 
succeeded  in  detecting  two  of  these  satellites.  In  1837, 
Lament,  with  the  powerful  refractor  of  the  royal  observa- 
tory of  Munich,  managed  to  follow,  with  tolerable  cer- 
tainty, the  two  larger  satellites,  and  occasionally  obtained 
glimpses  of  two  others. 

At  this  time  there  are  four  or  five  telescopes  in  the 
world  capable  of  showing  these  four  satellites,  under 
favorable  circumstances.  I  have  frequently  seen  two  of 
them  with  the  Cincinnati  refractor,  but  they  are  certainly 
objects  of  great  difficulty,  and  only  to  be  discerned  under 
the  most  favorable  circumstances  in  the  observer,  and 
under  the  best  possible  conditions  of  atmosphere. 

Enough,  however,  has  been  determined  with  reference 
to  these  four  satellites  to  warrant  the  assertion  of  a  fact 
of  most  extraordinary  character,  and  nowhere  else  to  be 
found  in  the  whole  range  of  the  solar  system,  namely, 
that  their  orbits  are  nearly  perpendicular  to  the  plane 
of  the  ecliptic,  and  that  their  motions  are  retrograde. 
We  have  seen  that  all  the  planets  revolve  in  orbits  whose 
planes  are  nearly  coincident  with  the  plane  of  the  eclip- 


262  URANUS. 

tic ;  that  they  all  revolve  in  the  same  direction  around  the 
sun ;  that  the  sun  and  all  the  planets  rotate  on  their 
axes  in  the  same  direction  in  which  they  revolve  in  their 
orbits.  We  have  found,  in  like  manner,  that  all  the  satel- 
lites of  every  planet  revolve  around  their  primaries  in 
the  same  direction,  and  in  planes  nearly  coincident  with 
the  planes  of  the  equators  of  their  primaries  ;  so  that  it 
became  a  settled  opinion  that  there  was  but  one  direction 
in  which  any  rotation  or  revolution  could  be  performed 
by  a  member  of  the  planetary  system ;  and  thus  when  the 
asteroids  were  discovered,  although  there  were  consider- 
able deviations  in  the  angles  of  the  inclination  of  the 
planes  of  their  orbits  from  those  of  the  old  planets,  yet 
in  every  instance  their  motions  are  found  to  be  direct. 
These  satellites  of  Uranus  present,  then,  the  only  example 
of  retrograde  movement  among  the  legitimate  members 
of  the  solar  system.  We  shall  see  hereafter  that  among 
the  comets  (which  may  be  regarded  as  satellites  of  the 
sun)  there  are  a  few  which  present  this  same  anomaly  of 
retrograde  movement,  yet  this  is  not  nearly  so  surprising 
as  to  find  this  anomalous  motion  among  the  satellites  of 
a  primary  planet.  We  shall  return  to  the  consideration 
of  this  subject  when  we  come  to  discuss  the  cosmogony 
of  the  universe. 

If  we  recall  to  mind  the  relations  which  exist  between 
the  distances  and  periodic  times  of  Uranus  and  Saturn, 
we  shall  find  that  these  two  planets,  when  nearest  to  eacn 
other,  or  when  in  conjunction,  are  separated  by  a  distance 
of  about  nine  hundred  millions  of  miles.  When  most 
remote  from  each  other,  this  distance  of  separation  is  in- 
creased by  the  whole  diameter  of  the  orbit  of  Saturn,  or 
by  eighteen  hundred  millions  of  miles,  as  will  be  readily 
seen  from  the  figure,  in  which  S  represents  the  sun, 


UB  ANUS. 


263 


A  and  B  the  places  of  Saturn  and  Uranus  when  in  con- 
junction, while  B'  represents  the  place  of  Uranus  in  the 
opposite  part  of  its  orbit,  or  when  in  opposition  to  the  sun. 
Thus  the  distance  between  the  planets  when  located  *c 


A  and  B  is  just  equal  to  the  interval  between  their 
orbits,  while  this  interval  is  increased  as  Uranus  recedes 
from  B  up  to  the  time  that  it  reaches  B',  and  on  reaching 
this  point,  Saturn  being  supposed  to  occupy  the  point  A, 
the  two  planets  will  be  separated  by  a  distance  of  about 
twenty-seven  hundred  millions  of  miles.  Since  Saturn 
performs  its  revolution  in  about  twenty-nine  years  and  a 
half,  and  Uranus  performs  its  revolution  in  about  eighty- 
two  years,  the  interval  from  one  conjunction  to  the  next 
is  readily  computed  to  be  about  forty  years. 

This  extraordinary  change  of  distance  produces  a  cor- 
responding change  in  the  reciprocal  influences  exerted  by 
these  planets  upon  each  other.  The  same  remark  is  ap- 
plicable to  the  configurations  of  Jupiter  and  Uranus,  and 
may  be  extended  indeed  to  all  the  planets.  Thus  we 
perceive  that  the  greatest  possible  effect  to  draw  Uranus 
closer  to  the  sun  will  be  produce!  when  all  tf  *  planets 


264  URANUS. 

lie  on  the  same  straight  line,  and  on  the  same  side  of  tho 
sun. 

The  prevalence  of  the  law  of  universal  gravitation, 
whereby  every  particle  of  matter  in  the  universe  feels  the 
attraction  of  every  other  particle,  unites  all  the  planets  and 
their  satellites  into  one  grand  scheme  of  revolving  worlds, 
in  which  each  is  subjected  to  the  influence  of  all  the 
others.  After  the  discovery  of  Uranus  an  effort  was 
made  to  assign  to  this  planet  a  curve  whose  magnitude 
and  position  were  derived  from  observations  embracing 
but  a  small  portion  of  its  orbit.  This,  of  course,  was 
a  matter  of  necessity,  for  even  one  revolution  has  not 
yet  been  completed  by  Uranus  since  the  date  of  its  dis- 
covery in  1781.  The  orbit  assigned  to  the  planet  was 
sufficiently  accurate  to  trace  backward  its  movement 
among  the  fixed  stars.  This  was  done  in  the  hope  that 
the  planet  might  have  been  seen  and  its  place  recorded 
as  a  fixed  star  by  some  of  the  early  astronomers.  If  it 
should  happen  that  the  computed  place  of  the  planet 
should  coincide  with  the  recorded  place  of  a  star  of  the 
same  magnitude  as  the  planet,  then  a  suspicion  would 
arise  that  this  star  and  the  planet  were  one  and  the  same 
body.  If  on  directing  the  telescope  to  the  point  once 
occupied  by  the  star  the  place  should  be  found  vacant, 
this  evidence  would  be  almost  conclusive  that  the  sup- 
posed star  was  actually  the  planet.  By  an  examination 
of  this  kind  it  was  found  that  the  planet  Uranus  had  been 
observed,  and  its  place  carefully  recorded  by  no  less  than 
three  astronomers,  each  of  whom  had  seen  it  several 
times,  without  any  suspicion  of  its  planetary  character. 
The  astronomer  Flamsteed  was  the  first  who  had  mistaken 
this  planet  for  a  star  nearly  ninety  years  before  its  dis- 
covery by  Sir  William  Herschell.  It  was  subsequently 


URANUS.  265 

observed  by  Bradley,  by  Mayer,  and  by  Le  Monnier, 
who  fixed  its  place  no  less  than  twelve  times  during  the 
period  from  1750  to  1771.  These  ancient  observations 
furnished  an  opportunity  to  test  the  accuracy  of  the  com- 
puted elements  of  the  orbit  of  the  new  planet,  and  to  cor- 
rect these  elements  in  case  they  were  found  to  be  sensibly 
in  error.  This  work  was  executed  in  a  most  faithful  and 
exact  manner  by  M.  Bouvard,  who  also  computed  tables 
predicting  the  places  of  Uranus  for  many  years  in  ad- 
vance. It  was  supposed  with  reason  that  these  tables 
would  point  out  the  places  of  Uranus  with  the  same  cer- 
tainty as  those  of  Saturn  and  Jupiter,  computed  by  the 
same  astronomer,  gave  the  places  of  these  planets.  In 
this  the  hopes  of  the  astronomical  world  were  disap- 
pointed, and  this  extraordinary  discrepancy  between  com- 
putation and  observation  gave  rise  to  the  discovery  of  an 
exterior  planet,  as  we  shall  now  relate. 

12 


CHAPTER    XIII. 

HEPTUNE,   THE  NINTH    AND    LAST    KNOWN    PLANET    IN 
THE  ORDER  OF  DISTANCE  FROM  THE   SUN. 

UBANTTB  DISCOVERED  BY  ACCIDENT.— CERES  BY  EESEARCH  WITH  THE  TELESCOPE. 
— REDISCOVERED  BY  MATHEMATICAL  COMPUTATION. — THE  PERTURBATIONS 
OF  URANUS. — NOT  DUE  TO  ANY  KNOWN  CAUSE. — ASSUMED  TO  ARISE  FROM 
AN  EXTERIOR  PLANET. — MATURE  OF  THE  EXAMINATION  TO  FIND  THE  UN- 
KNOWN PLANET — UNDERTAKEN  AT  THE  SAME  TIME  BY  TWO  COMPUTERS. — 
COMPUTATION  ASSIGNS  A  PLACE  TO  THE  UNKNOWN  PLANET. — DISCOVERED 
BY  THE  TELESCOPE. — DISCOVERIES  RESULTING. — A  SATELLITE  DETECTED.— 
THK  MASS  OF  NEPTUNE  THUS  DETERMINED.— NEPTUNE'S  ORBIT  THE  CIRCUM- 
SCRIBING BOUNDARY  OF  THE  PLANETARY  SYSTEM. 

THE  discovery  of  Neptune  is  undoubtedly  the  most 
remarkable  event  in  the  history  of  astronomical  science — 
an  event  without  a  parallel,  and  rising  in  grandeur  pre- 
eminently above  all  other  efforts  of  human  genius  ever  put 
forth  in  the  examination  of  the  physical  universe. 

The  planet  Uranus  was  discovered  by  the  aid  of  the 
telescope,  not  exactly  by  accident,  but  still  without  any 
expectation  on  the  part  of  the  discoverer  that  his  examina- 
tion of  the  fixed  stars  would  result  in  the  addition  of  a 
primary  planet  to  the  system.  Indeed,  as  we  have  seen, 
so  little  did  the  astronomical  world  then  anticipate  the 
discovery  of  a  new  planet  that  the  announcement  by  Si'r 
William  Herschel  that  he  had  detected  a  most  remarkable 
comet  was  accepted  on  all  hands,  and  it  was  only  con- 
tinued observation  that  finally  compelled  astronomers  to 


NEPTUNE.  267 

accept  the  new  object  as  a  planet.  In  the  case  of  the 
discovery  of  the  first  asteroid  we  find  a  systematic  organ- 
ization of  astronomical  effort  to  detect  a  body  whose  exist- 
ence was  conjectured,  on  the  single  ground  of  the  har- 
mony of  the  universe,  or  that  the  law  of  interplanetary 
spaces,  interrupted  between  Mars  and  Jupiter,  would  be 
restored  by  finding  a  planet  revolving  within  that  vast 
interval.  Hence  a  search  was  commenced  which  con- 
sisted in  examining  every  star  in  the  region  of  the  eclip- 
tic, to  ascertain  whether  its  place  was  already  laid  down 
on  any  known  map  or  chart  of  the  heavens.  Now  it  is 
evident  that  if  it  were  possible  to  make  a  perfect  daguer- 
reotype of  any  region  of  the  celestial  sphere,  say  to-night, 
and  the  same  could  be  effected  on  the  following  night, 
the  comparison  of  these  two  pictures  would  exhibit  to  the 
eye  any  change  which  may  have  occurred  in  the  interval 
from  the  one  picture  to  the  other ;  and  hence  if  a  star 
was  found  on  the  second  and  not  on  the  first  picture, 
this  star  might  fairly  be  suspected  to  be  a  planet,  or  the 
same  suspicion  would  attach  to  a  star  found  on  the  first, 
but  missing  on  the  second  picture.  Now,  a  map  of  the 
heavens,  so  far  as  it  includes  the  correct  places  of  the 
stars,  answers  our  purpose  quite  as  well  as  the  daguerreo- 
type, and  any  star  found  in  a  region  well  charted,  but 
not  laid  down  on  the  map,  may  be  fairly  suspected  to  be 
a  planet.  A  few  hours  of  examination  will  show  it  to  be 
at  rest  or  in  motion.  If  in  motion,  then  its  planetary 
character  is  decided. 

This  method  of  research  has  been  employed  in  the  dis- 
covery of  all  the  asteroids,  and  there  is  but  one  example 
in  which  a  more  powerful  and  searching  examination  be- 
came necessary.  This  was  in  the  case  of  the  asteroid 
Ceres,  which,  as  we  have  seen,  was  discovered  by  Piazzi, 


268  NEPTUNE. 

at  a  time  when  but  few  observations  could  be  made  previ- 
ous to  its  being  lost  in  the  rays  of  the  sun.  For  a  long 
time  it  seemed  almost  a  hopeless  task  to  undertake  the 
re-discovery  of  the  planet,  as  the  telescope  would  be  com- 
pelled to  grope  its  way  slowly  round  the  heavens,  in  the 
region  of  the  ecliptic,  comparing  every  star  with  its  place 
in  the  chart.  In  this  dilemma  mathematical  analysis 
essayed  to  erect  a  structure  on  the  narrow  basis  of  the 
few  observations  obtained  by  Piazzi,  whereon  the  instru- 
mental astronomer  might  stand  and  point  his  telescope  to 
the  precise  point  occupied  by  the  lost  planet.  The  genius 
of  Gauss  succeeded  in  this  herculean  task,  and  when  the 
telescope  was  pointed  to  the  heavens  in  the  exact  place 
indicated  by  the  daring  computer,  there,  in  the  field  of 
view,  shone  the  delicate  and  beautiful  light  of  the  long- 
lost  planet. 

This  was  certainly  a  most  wonderful  triumph  of  analytic 
reasoning,  yet  in  this  case  the  planet  had  been  discovered, 
was  known  to  exist,  and  had  been  observed  over  4°  out 
of  the  360°  of  its  revolution  round  the  sun.  On  this 
basis  of  4°  it  was  possible  to  rise  to  a  knowledge  of  the 
planet's  position  at  the  end  of  a  few  months  of  time. 

The  case  of  the  discovery  of  Neptune  is  entirely  differ- 
ent. Here  no  planet  was  known  to  exist,  no  telescopic 
power,  however  great,  had  ever  seen  it.  For  ages  it  had 
revolved  round  the  sun  in  its  vast  orbit,  far  beyond  the 
utmost  known  verge  of  the  planetary  system,  unfathom- 
ably  buried  from  human  gaze  and  from  human  knowl- 
edge. No  sage  of  antiquity  had  ever  dreamed  of  its  ex- 
istence. The  fertile  brain  of  even  Kepler  had  failed  to 
imagine  its  being,  and  the  powerful  penetration  of  New- 
ton's gigantic  intellect  had  failed  to  pierce  to  the  far  off 
region  inhabited  by  this  unknown  and  solitary  planet. 


NEPTUNE.  269 

Indeed,  with  the  knowledge  which  existed  prior  to  the 
discovery  of  Uranus,  no  human  genius,  however  mighty, 
could  have  passed  the  tremendous  interval  which  separates 
the  orbits  of  Saturn  and  Neptune  from  each  other.  The 
discovery  of  an  intermediate  planet  was  requisite  to  fur- 
nish a  firm  foothold  to  him  who  would  adventure  to  pass 
a  gulf  of  not  less  than  2,000  millions  of  miles  at  its  nar- 
rowest place. 

We  shall  now  proceed  to  relate  the  circumstances 
which  led  to  the  discovery  of  Neptune.  As  already 
stated,  a  careful  and  elaborate  study  of  the  orbit  of 
Uranus  had  been  accomplished  by  M.  Bouvard,  and 
tables  giving  the  computed  places  of  this  planet  had  been 
prepared  by  the  same  astronomer.  It  was  not  antici- 
pated that  these  tables  would  be  absolutely  perfect,  even 
if  based  on  perfect  observations.  We  must  remembei 
that  each  body  of  the  solar  system  affects  every  other, 
and  hence  no  single  set  of  observations  are  sufficient  to 
give  a  perfect  orbit.  In  case  all  the  other  worlds  were 
blotted  out  of  existence,  and  there  remained  only  the 
sun  and  Uranus,  then  three  perfect  observations  of  the 
planet's  place  would  suffice  to  determine  positively  all 
the  elements  of  its  orbit,  and  fix  forever  all  the  circum- 
stances of  its  motion.  We  shall  call  the  figure  of  the 
orbit  of  Uranus,  obtained  under  the  above  hypothesis, 
the  normal  figure,  and  the  ellipse  which  it  would  de- 
scribe about  the  sun,  under  the  above  circumstances,  the 
normal  ellipse.  If  now  we  introduce  another  planet 
into  our  system,  as,  for  example,  Saturn,  it  is  possible, 
as  we  have  already  seen,  to  compute  the  exact  amount  of 
power  exerted  by  Saturn  to  disturb  the  movements  of 
Uranus,  and  to  change  the  figure  of  its  orbit.  In  like 
manner,  by  adding  successively  all  the  interior  planets, 


270  NEPTUNE. 

it  is  possible  to  compute  the  perturbations  that  each  pro- 
duces upon  the  orbit  of  any  particular  one,  until,  finally, 
by  using  all  the  power  of  analytic  reasoning,  the  human 
mind  may  reach  to  a  complete  knowledge  of  all  possible 
derangements  produced  by  the  combined  action  of  all  ex- 
isting known  causes  of  perturbation. 

Supposing  our  knowledge  in  this  way  to  become  per- 
fect as  to  the  movements  and  orbit  of  Uranus,  we  can 
then  predict  its  places  in  all  coming  time,  and  these  pre- 
dictions, being  arranged  in  tabular  form,  may  be  verified 
by  comparison  in  after  years  with  the  observed  places  of 
the  planet.  If  now  a  new  planet  were  added  to  the  sys- 
tem, revolving  in  an  orbit  exterior  to  that  of  Uranus, 
perturbation  would  arise  from  the  introduction  of  this 
disturbing  body  into  our  system  which  would  at  once 
cause  the  planet  to  deviate  from  its  predicted  track,  and 
the  observed  and  computed  places  would  no  longer  agree. 

We  can  perceive  at  once,  from  this  statement  of  the 
problem,  that  these  very  discrepancies  between  the  old 
track  and  the  new  one,  pursued  by  the  planet,  would 
give  us  a  clue  whereby  it  might  become  possible  to  de- 
termine, in  space,  the  position  of  the  disturbing  body.  „ 

Difficult  and  incomprehensible  as  the  above  problem 
may  appear,  it  is  far  less  difficult  than  the  one  actually 
presented  in  nature.  We  have  supposed  the  normal 
ellipse,  described  by  Uranus,  to  be  known,  whereas,  in 
reality,  this  very  ellipse  had  to  be  determined  by  a  train 
of  reasoning  of  the  most  searching  and  powerful  charac- 
ter, while  the  whole  problem  was  almost  hopelessly  em- 
barassed  by  the  fact  that  the  movements  of  Uranus  were 
actually  being  disturbed  all  the  time  by  the  unknown 
body  whose  position  in  space  was  required.  As  the 
normal  orbit  could  only  be  determined  by  a  series  of  ap- 


NEPTUNE.  271 

proximations,  based  upon  the  observed  places  of  the  planet, 
it  was  impossible,  in  any  one  of  these  approximations,  to 
free  Uranus  from  the  disturbing  effects  of  the  unknown 
body.  It  was  only,  therefore,  by  comparing  with  each 
other  the  results  reached  by  these  successive  approxima- 
tions to  the  orbit  of  Uranus  that  it  became  manifest  that 
no  increase  of  accuracy  was  being  reached  by  these  suc- 
cessive efforts,  and  after  every  known  cause  of  disturb- 
ance had  been  carefully  taken  into  account,  a  grand  con- 
clusion was  finally  reached  that  no  satisfactory  account 
could  be  rendered  of  the  movements  of  Uranus  by  the 
combined  effects  of  all  known  disturbing  causes. 

To  reach  this  conclusion  required  investigations  of  the 
most  profound  and  laborious  character,  but  before  it  ffaa 
possible  to  explain  these  anomalous  movements  of  Ura>ius, 
a  problem  of  far  greater  difficulty  remained  to  be  solved, 
involving  nothing  less  than  a  determination  of  the  weight 
of  the  unknown  planet,  its  distance  from  the  sun,  the 
nature  of  its  orbit,  and  its  position  in  the  heavens  at  a 
particular  time,  indicating  the  region  to  which  the  tele- 
scope must  be  pointed  to  render  visible  what  had  hitherto 
remained  for  ages  unseen  by  the  eye  of  man. 

To  those  who  have  given  but  little  attention  to  the 
study  of  these  extraordinary  problems  an  attempt  to  re- 
solve a  question  like  that  just  presented  may  seem  to  be 
even  presumptuous,  yet  when  we  come  to  examine  the 
circumstances,  we  shall  see  dimly  a  way  whereby  we  may 
reach  a  certain  approximate  knowledge  of  the  place  of 
this  unknown  "world. 

The  fact  that  the  planes  of  the  orbits  of  all  the  more 
distant  planets  are  nearly  coincident  with  the  ecliptic  re- 
duced the  examination  to  the  great  circle  in  the  heavens 
cut  out  by  the  indefinite  extension  of  this  plane.  This 


272  NEPTUNE. 

is  a  most  important  consideration,  and  but  for  this  fortu- 
nate circumstance  no  powers  of  research  could  ever  have 
made  even  the  most  distant  approximation  to  the  place  of 
the  unknown  planet. 

The  empirical  law  of  Bode,  whereby  it  seemed  that 
the  order  of  distances  of  the  planets  was  governed,  as- 
signed to  the  hypothetical  world  a  distance  about  double 
that  of  Uranus,  or  say,  3,600  millions  of  miles  from  the 
sun.  Assuming  this  as  the  probable  distance,  the  third 
of  Kepler's  laws  would  determine  the  period  of  revolution 
of  the  world  whose  position  was  sought.  It  remained 
now  to  assign  a  mass  and  position  to  the  planet  such  as 
would  render  a  satisfactory  account  of  the  perturbations 
of  Uranus,  which  remained  outstanding  after  the  known 
causes  of  disturbance  were  exhausted.  To  accomplish 
this  let  us  recall  to  mind  the  fact  that  in  case  the  mean 
distance  of  the  disturbing  body  had  been  rightly  selected, 
then  the  interval  between  Uranus  and  the  unknown, 
when  in  conjunction,  would  be  about  1,800  millions  of 
miles.  In  this  position  the  disturbing  force  would  exhi- 
bit its  maximum  power  in  a  twofold  sense :  first,  to 
cause  Uranus  to  recede  to  its  greatest  distance  from  the 
sun ;  and,  second,  to  cause  the  same  planet  to  lag  behind 
the  place  it  would  otherwise  have  reached.  In  the 
above  figure  let  U  U'  U"  represent  the  computed  orbit 
of  Uranus,  as  existing  under  the  combined  influence  of 
all  known  causes,  P  the  place  of  the  unknown,  when  in 
conjunction  with  Uranus  at  U'.  It  is  manifest  that  the 
force  exerted  by  P  on  Uranus  will  tend  to  accelerate  its 
velocity  in  coming  up  to  conjunction,  and  to  cause  the 
path  described  to  lie  outside  the  computed  path  along  the 
dotted  line,  the  planet  really  reaching  the  point  U"',  in- 


NEPTUNE. 


273 


Btead  of  U'  in  the  undisturbed  orbit.  Leaving  this  point 
the  force  exerted  b^  the  unknown  would  reverse  its 
effect,  and  a  retardation  would  commence,  and  by  slow 


degrees  receding  from  the  disturbing  body,  it  would 
gradually  return  to  the  undisturbed  orbit,  and  there  con- 
tinue until  the  period  for  the  next  conjunction  might 
approach. 

Such  is  a  rough  exhibition  of  the  reasoning  which  was 
emplo .  ed  to  narrow  the  limits  of  research  in  the  effort 
to  point  the  telescope  to  the  unknown  cause  of  the  per- 
turbations of  Uranus.  No  account,  of  course,  can  be 
given  of  the  mathematical  treatment  of  the  problem.  It 
was  undertaken  at  about  the  same  time  by  Adams,  of 
England,  and  by  Le  Verrier,  of  Paris.  Each  computer, 
unknown  to  the  other,  reached  a  result  almost  identical. 
Le  Verrier  communicated  his  solution  to  the  Academy 
of  Sciences  on  the  31st  August,  1847,  and  on  the  even- 
ing of  the  18th  September,  1847,  M.  Galle,  of  Berlin 
directed  the  telescope  to  the  point  in  which  the  French 
geometer  declared  the  unknown  planet  would  be  found 

12* 


274  NEPTUNE. 

A  star  of  the  eighth  magnitude  appeared  in  the  field  of 
view,  whose  place  was  not  laid  down  on  any  known 
chart.  Suspicion  was  at  once  aroused  that  this  might 
possibly  be  the  planet  of  computation,  and  yet  it  seemed 
incredible  that  a  problem  far  surpassing  in  difficulty  any 
which  had  ever  been  attempted  by  human  genius  should 
thus  at  the  first  effort  have  been  solved  with  such  mar- 
velous precision. 

The  suspected  star  was  examined  with  the  deepest  in- 
terest in  the  hope  that  it  might  exhibit  a  planetary  disk. 
In  this,  however,  the  astronomer  was  unsuccessful,  and 
there  remained  but  one  method  by  which  its  planetary 
character  might  be  determined,  that  of  watching  suf- 
ficiently long  to  detect  its  motion.  This  process,  how- 
ever, must  have  tried  very  sorely  the  patience  of  the  ob- 
server, as  the  motion  of  the  planet  at  so  great  a  dis- 
tance as  three  thousand  six  hundred  millions  of  miles, 
was  so  slow  as  to  require  three  entire  months  to  pass 
over  a  space  equal  to  the  apparent  diameter  of  the 
moon.  The  position  of  the  suspected  star  having  been 
accurately  determined  on  the  first  night  of  observation, 
it  became  evident  on  the  next  night  that  the  star  had 
moved  by  an  amount  such  as  was  fairly  due  to  the  slow 
motion  of  so  vast  an  orbit.  It  could  be  none  other  than 
the  unknown  planet !  A  success  almost  infinitely  beyond 
the  expectations  of  the  most  sanguine  computer  had 
crowned  this  mighty  effort,  and  the  amazing  intelligence 
that  the  planet  was  found  startled  the  astronomical 
world. 

The  planet  was  soon  recognized  by  the  astronomers  in 
every  part  of  the  world.  The  elements  assigned  by  Le 
Verrier  and  Adams  by  computation  were  accepted  every- 
where with  most  unhesitating  faith  in  their  accuracy,  and 


NEPTUNE.  275 

it  was  believed  that  it  only  remained  for  the  telescope  to 
verify  the  computations  of  these  most  wonderful  mathe- 
maticians. In  this  the  astronomical  world  were  destined 
to  meet  a  most  remarkable  disappointment.  The  new 
planet  proved,  indeed,  adequate  to  account  for  all  the 
anomalous  movements  of  Uranus,  while  in  all  its  ele- 
ments it  differed  so  widely  from  those  of  the  computed 
hypothetical  planet  that  the  computed  and  real  planet 
could  not  in  any  way  be  regarded  as  the  same  body. 
The  first  restriction  proved  to  be  correct,  for  the  orbit  of 
the  new  planet  (afterwards  named  Neptune)  did  coincide 
almost  exactly  with  the  plane  of  the  ecliptic.  The  second 
restriction,  based  on  the  extension  of  Bode's  law  of  in- 
terplanetary spaces,  was  falsified  in  the  event,  for  here 
the  law  of  Bode  failed,  and  the  distance  of  the  true 
planet  was  nearly  5,000  millions  of  miles  less  than  that 
of  the  computed  one. 

The  third  restriction  due  to  the  application  of  Kepler's 
third  law  is  verified  in  the  real  planet ;  but  as  the  dis- 
tance of  the  unknown  was  assumed  greatly  too  large,  of 
course  the  periodic  time  depending  on  this  distance  was 
also  too  large.  This  by  necessity  involved  an  error  in 
the  mass  assumed  for  the  unknown,  whose  erroneous  dis- 
tance demanded,  of  course,  an  erroneous  mass  greater  than 
that  of  the  true  planet;  and  yet,  notwithstanding  the 
magnitude  of  the  errors  of  these  elements,  the  computers 
succeeded  in  pointing  the  telescope  within  less  than  one 
degree  of  the  actual  plajce  of  the  body  which  had  caused 
the  anomalous  movements  of  Uranus  ! 

We  will  endeavor  to  render  a  brief  account  of  this 
most  astonishing  fact.  It  is  evident  that  the  disturbing 
effects  of  Neptune  will  become  most  powerful  when  the 
disturbing  planet  is  nearest  the  disturbed  one,  or,  what 


276  NEPTUNE. 

amounts  to  the  same  thing,  the  maximum  disturbance 
will  occur  when  the  planets  are  in  conjunction.  We 
know  that  the  periodic  time  of  Uranus  is  82  years,  the 
periodic  time  of  Neptune  is  164  years,  and  hence  it  is 
easy  to  compute  the  interval  from  one  conjunction  to  the 
next,  which  is  no  less  than  171  years.  The  two  planets 
passed  their  conjunction  in  1822,  and  therefore  the  pre- 
vious conjunction  must  have  occurred  171  years  before,  or 
in  1651 ;  but  the  earliest  recorded  observation  of  Uranus 
was  not  made  till  1690,  or  nearly  40  years  after  the 
conjunction,  and  at  a  time  when  the  disturbing  force  of 
Neptune  was  so  much  diminished  as  to  be  nearly,  if  not 
quite  insensible,  for  a  long  while.  The  minute  disturbing 
power  of  Neptune  still  existing  in  1690,  would  go  on 
decreasing  until,  in  1732,  the  planets  would  be  in  oppo- 
sition, and  would  be  separated  by  a  maximum  interval. 
After  this  date  the  distance  between  the  planets  would 
slowly  decrease  as  they  approached  their  conjunction, 
and  in  1781,  when  Uranus  was  discovered,  a  small  dis- 
turbing effect  would  begin  to  be  appreciable,  which  would 
go  on  increasing  up  to  the  time  of  conjunction  in  1822. 
Thus  we  perceive  that  mathematicians  found  the  planet 
Uranus  in  such  condition  that  the  perturbing  effects  of 
Neptune  were  increasing  in  intensity  from  year  to  year  ; 
and  hence  no  set  of  elements  could  correctly  represent 
the  places  of  Uranus,  because  the  observations  did  not 
extend  back  far  enough  to  embrace  the  disturbed  places 
of  the  planet  at  the  former  conjunction  in  1651.  No  cor- 
rect solution  was  then  possible  "until  the  perturbations 
should  reach  their  maximum  value,  which  occurred  in 
1822,  when  the  planets  were  in  conjunction,  and  subse- 
quent to  which  period  the  planet  Uranus  would  slowly 
return  to  its  computed  orbit  as  it  receded  further  and 


NEPTUNE. 


277 


still  further  from  the  influence  of  the  disturbing  body,  aa 
may  be  more  clearly  seen  from  the  figure  below,  in  which 
the  smaller  circle  may  represent  the  orbit  of  Uranus,  the 
larger  one  the  orbit  of  Neptune.  For  a  long  while  prior 


N 


to  conjunction  in  1822,  Uranus  would  be  slowly  over- 
taking Neptune,  during  which  time  the  direction  of  the 
disturbing  force  would  be  such  as  to  accelerate  the  orbital 
motion  of  Uranus,  and  to  increase  its  distance  from  the 
sun.  The  acceleration  would  cease  at  conjunction,  and 
would  there  be  changed  into  equal  and  opposite  retarda- 
tion, as  is  manifest  from  the  figure,  while  the  increase  of 
the  distance  of  Uranus  must  continue  to  increase  even 
after  conjunction,  but  the  disturbing  force  must  rapidly 
decline  in  power  as  the  interval  between  the  planets  in- 
creases. Thus  the  great  problem  demanded  the  position 
of  a  disturbing  planet  at  a  given  time,  which  could  ac- 
count for  the  known  perturbations,  all  of  which  were 


278  NEPTUNE. 

crowded  into  a  few  years,  say  25,  before  and  after  the 
conjunction  in  1822.  While  this  narrowing  of  the  limits 
of  sensible  perturbation  increased  the  chances  of  direct- 
ing the  telescope  to  the  unknown  disturber,  it  seems  to 
have  really  increased  the  difficulty  of  assigning  to  this 
disturber  his  exact  orbit.  Indeed,  even  with  circular 
orbits,  several  might  have  been  chosen,  such  that  by  vary- 
ing the  mass  of  the  unknown  the  perturbations  might 
have  been  tolerably  well  represented,  but  in  case  ellip- 
tical orbits  are  chosen,  then  our  limits  are  much  extended, 
and  the  mean  distance  may  be  made  to  vary  within  very 
broad  limits,  provided  the  eccentricity  may  be  chosen  at 
pleasure.  Thus  the  ellipse  shown  in  the  figure  coincides 
between  N  and  N'  very  nearly  with  the  circular  orbit, 
and  in  case  a  planet  revolving  in  the  circle  could  account 
for  the  anomalies  of  Uranus,  the  same  would  be  tolerably 
well  represented  by  the  effects  of  a  planet  with  a  very 
different  period  and  mean  distance  revolving  in  the  ellip- 
tic orbit.  Now  this  was  exactly  the  case  as  developed  in 
the  final  history  of  this  grand  discovery.  The  great  geo- 
meters chose  an  elliptic  orbit  of  such  eccentricity  and 
having  its  major  axis  in  such  position  that  the  computed 
and  true  orbits  agreed  with  each  other  in  a  most  remark- 
able manner  during  the  twenty  years  before  and  after 
conjunction.  Their  efforts  were  thus  crowned  with  the 
success  which  they  so  eminently  deserved  •  and  although 
the  computed  orbit  came  finally  to  differ  greatly  from  the 
true  one,  yet,  for  the  time  when  the  computed  orbit  was 
required  to  represent  the  places  of  the  unknown,  and  to 
point  the  telescope  to  its  actual  location,  the  computed 
orbit  responded  nearly  as  perfectly  as  the  true  one  could 
have  done,  even  had  it  been  then  known. 

It  has  been  already  stated  that  after  the  discovery  of 


NEPTUNE.  279 

Uranus,  when  the  elements  of  its  orbit  had  heen  obtained 
with  sufficient  accuracy  to  render  it  possible  to  trace  the 
planet  backwards  among  the  fixed  stars,  it  was  ascertained 
that  it  had  been  observed  and  its  place  recorded  as  early 
as  1690,  and  had  been  seen  many  times  subsequently  and 
prior  tc  its  discovery,  being  always  mistaken  for  a  fixed 
star,  so  we  find  in  the  case  of  Neptune,  a  like  examina- 
tion by  Professor  Walker  led  to  the  discovery  that  the 
new  planet  had  been  twice  recorded  in  position  by  La 
Lande,  in  May,  1795.  These  two  observations  were 
found  to  be  outside  the  path  which  had  been  assigned  the 
plantt  by  the  theory  of  both  Le  Verrier  and  Adams  ;  and 
such  was  the  deep  confidence  in  the  accuracy  of  the  ele- 
ments assigned  by  these  two  geometers  that  it  was  with 
great  difficulty  that  some  of  the  ablest  astronomers  could 
be  induced  to  believe  that  the  missing  star  twice  observed 
by  La  Lande  could  be  the  new  planet.  The  identity  was, 
however,  soon  demonstrated,  and  hence  arose  the  discus- 
sion which  led  to  the  declaration  by  an  eminent  mathe- 
matician that  the  discovery  of  Neptune  was  the  result  of 
a  happy  accident ;  but  we  have  seen  that  the  grand  pro- 
blem propounded  by  both  the  French  and  English  astrono- 
mer, and  which  each  resolved  with  such  astonishing  pre- 
cision, was  to  point  the  telescope  in  the  direction  of  the 
unknown,  which  had  produced  the  late  excessive  pertur- 
bations of  Uranus.  It  remains,  so  far  as  I  know,  yet  to 
be  decided  whether  the  data  in  possession  of  Adams  and 
Le  Verrier  can  be  so  treated  by  analysis  as  to  give  an 
orbit  to  the  unknown  more  nearly  agreeing  with  that  of 
the  known  planet. 

NEPTUNE'S  SATELLITE. — The  vast  distance  to  which 
Neptune  is  buried  in  space  will  perhaps  render  it  impos- 
sible to  learn  how  many  satellites  revolve  about  this  re- 


280  NEPTUNE. 

mote  primary.  The  great  refractors  have  certainly  dis- 
covered the  existence  of  one  satellite,  and  another  is 
suspected.  The  discovery  of  this  one  satellite  of  Neptune 
becomes,  under  all  the  circumstances,  a  matter  of  deep 
interest,  as  it  enables  us  to  determine  the  mass  or  weight 
of  the  primary,  a  matter  of  the  first  moment  in  comput- 
ing the  effects  of  the  planet  as  a  disturbing  body.  The 
satellite  is  found  to  perform  its  revolution  about  the 
primary  in  a  period  of  about  five  days  and  twenty-one 
hours,  and  at  a  mean  distance  of  232  thousand  miles,  or 
nearly  equal  to  the  distance  of  our  moon  from  the  earth. 
In  case  these  distances  are  assumed  to  be  exactly  equal, 
then  as  at  the  same  distance  the  centrifugal  force  in- 
creases as  the  square  of  the  velocity,  and  as  the  velocity 
of  Neptune's  moon  is  about  four  and  a  half  times  greater 
than  that  of  our  moon,  its  centrifugal  force  in  its  orbit  must 
be  4.5  x  4.5,  equal  to  about  twenty  times  the  centrifugal 
force  of  the  moon.  Now,  the  attractive  force  of  Nep- 
tune is  exactly  proportioned  to  its  weight  or  mass,  and 
hence,  to  counterbalance  this  centrifugal  force  in  his  satel- 
lite, which  is  twenty  times  as  great  as  that  of  the  moon, 
the  mass  of  Neptune  must  be  twenty  times  as  great  as 
that  of  the  earth.  Thus  has  been  revealed  not  one 
world,  but  two — the  one  containing  a  mass  of  matter 
sufficient  to  form  no  less  than  twenty  worlds  as  heavy  as 
our  earth — the  other  a  satellite,  indeed,  of  the  first,  yet 
sufficiently  large  to  send  back  to  us,  at  a  distance  of 
3,000  millions  of  miles,  the  light  of  the  sun,  enfeebled 
by  its  dispersion  over  this  vast  distance  to  the  one- 
thousandth  part  of  the  intensity  it  pours  on  our  earth. 
We  have  reached  the  known  boundary  of  that  mighty 
confederation  of  revolving  orbs  which,  whilst  they  ac- 
knowledge in  the  most  specific  manner  a  mutual  depend- 


NEPTUNE.  281 

ence,  are  all  controlled  by  the  predominating  influence 
of  the  sun,  which  occupies  the  common  focus  of  all  their 
orbits,  and  around  which  they  all  roll  and  shine  in  obedi- 
ence to  the  grand  law  of  universal  gravitation. 

"We  shall  now  retrace  our  steps  toward  the  sun,  and 
consider  a  remarkable  class  of  bodies,  which  for  ages  were 
regarded  as  evanescent  meteors,  suddenly  blazing  athwart 
the  sky,  and  as  suddenly  fading  from  the  vision,  never 
more  to  reappear.  Modern  science  has  given  to  these 
bodies  determinate  orbits,  and  in  some  instances,  as  we 
shall  see,  has  assigned  them  a  permanent  place  among  the 
satellites  of  the  sun. 


CHAPTER   XIV. 


THE   COMETS. 


OBJECTS  OF  DREAD  IN  TITE  EARLY  AGES. — COMETS  OBEY  THE  LATV  OF  GRK? r- 

TATION  AND  REVOLVE  IN  SOME  ONE  OF  THE  CONIC  SECTIONS. — CHARACTER- 
ISTICS OF  THESE  CURVES.— COMET  OF  1680  STUDIED  BY  NEWTON.— COMET  OF 
1632  NAMED  "  II ALLEY'S  COMET."— ITS  HISTORY.— ITS  RETURN  PREDICTED. 
PERIHELION  PASSAGE  COMPUTED. — PASSES  ITS  PERIHELION  18TH  APRIL, 
1759. — ELEMENTS  OF  ITS  ORBIT. — PHYSICAL  CONSTITUTION. — NUCLEUS. — EN- 
VELOPES.—TAIL.— INTENSE  HEAT  SUFFERED  BY  SOME  COMETS  IN  PERIHELIO. 
—DISSIPATION  OF  THE  COMETIO  MATTER.— ENCKE'S  COMET.— A  RESISTING 
MEDIUM.— DEDUCTIONS  FROM  OBSERVATION.— BIELA'S  COMET.— DIVIDED.— 
NUMBER  OF  COMETS. 


UN  all  ages  of  the  world  these  anomalous  objects  have 
excited  the  deepest  interest,  not  only  among  philosophers, 
but  among  all  classes  of  men.  The  suddenness  with 
which  they  sometimes  blaze  in  the  sky,  the  vast  dimen- 
sions of  their  fiery  trains,  the  exceeding  swiftness  with 
which  they  pursue  their  journey  among  the  stars,  the 
rapid  disappearance  of  even  the  grandest  of  these  seeming 
chaotic  worlds,  have  all  combined  to  invest  these  bodies 
with  a  power  to  excite  a  kind  of  superstitious  terror  which 
even  the  exact  revelations  of  science  cannot  wholly  dis- 
pel. History  records  the  appearance  of  these  phenomena, 
and  in  general  they  were  regarded  as  omens  of  some 
terrible  scourge  to  mankind,  the  precursors  of  war  or 
pestilence  or  famine,  or  at  the  very  least  announcing  the 
death  of  some  prince  or  potentate.  Some  of  the  ancients, 
of  course,  rose  above  these  superstitious  ideas,  and  the 


THE    COMETS.  283 

Roman  philosopher  Seneca  even  entertained  the  opinion 
that  these  erratic  bodies  would  some  day  fall  within  the 
domain  of  human  knowledge,  that  their  paths  among  the 
stars  would  eventually  be  traced,  and  that  they  would  be 
found  in  the  end  to  be  permanent  members  of  the  solar 
system.  How  remarkably  this  prediction  has  been  veri- 
fied will  appear  in  the  concise  sketch  we  are  about  to 
present. 

The  discovery  of  ther  law  of  universal  gravitation  was 
followed  by  a  mathematical  demonstration,  also  accom- 
plished by  the  great  English  philosopher,  which  was  the 
reverse  of  the  problem  he  had  just  solved,  and  may  be 
announced  as  follows  :  Given,  the  intensity  of  a  fixed 
central  force,  decreasing  in  power  as  the  squares  of 
the  distances  increase,  and  the  direction  and  intensity 
of  an  impulsive  force  operating  to  set  in  motion  a 
body  subject  to  the  central  power :  Required,  the  na- 
ture and  figure  of  the  path  described  by  the  revolving 
body  ? 

Previous  to  the  resolution  of  this  problem  Newton 
naturally  expected  to  find  the  curve  sought  to  be  an 
ellipse.  The  sun  was  the  source  of  a  fixed  central  force 
which  obeyed  the  above  law.  The  planets  were  retained 
in  their  orbits  by  this  central  force.  These  described 
ellipses  in  their  revolution  around  the  sun,  and  it  was 
natural  to  Conclude  that  the  solution  of  the  inverse  pro- 
blem would  lead  to  the  elliptic  orbit.  On  completing  the 
solution  and  reaching  the  mathematical  expression  repre- 
senting the  orbit,  it  was  found  not  to  be  the  usual  ex- 
pression for  the  ellipse,  and  after  careful  examination 
proved  to  be  the  general  expression,  embracing  within  its 
grasp  no  less  than  four  curves,  the  circle,  the  ellipse,  the 
parabola,  and  the  hyperbola.  These  curves  are  allied  in 


234 


THE     COMETS. 


a  most  remarkable  manner,  having  certain  properties  in 
common,  and  having  in  one  sense  a  common  origin. 
They  may  all  be  obtained  by  cutting  the  surface  of  a  cone 
by  a  plane  passing  in  different  directions,  as  may  be  seen 
from  the  figure  below.  Let  A  be  the  vertex,  and  C  D  E 


L  the  circular  base  of  a  cone  seen  obliquely.  Any  plane 
passed  parallel  to  the  base,  or  perpendicular  to  the  axis 
A  B,  will  cut  from  the  surface  a  circle,  as  F  E  G.  A 
plane  passed  obliquely  to  the  axis  will  cut  from  the  sur- 
face an  ellipse,  as  M  0  0'.  Any  plane  passed  parallel 
to  the  side  of  the  cone  A  C  will  cut  the  curve  T  W  X, 
called  a  parabola,  and  any  plane  passed  parallel  to  the 


THE     COMETS.  285 

axis  of  the  cone  A  B  will  cut  out  from  the  surface  the 
curve  K  I  L,  called  an  hyperbola.  These  curves  are 
thus  all  derived  from  the  conic  surface  by  intersecting 
it  with  a  plane,  and  are  hence  called  conic  sections. 
Now,  a  little  examination  will  show  us  that  while  the 
circle  and  ellipse  are  re-entering  curves  of  limited  ex- 
tent, this  is  not  the  case  with  the  parabola  and  hyper- 
bola. If  the  conic  surface  were  indefinitely  extended 
below  the  base,  it  is  evident  that  the  cutting  plane  X  W  T, 
being  parallel  to  the  side  A  C,  could  never  cut  that  par- 
ticular line,  and  hence  the  parabola,  departing  from  the 
point  W,  and  passing  through  T  and  X,  would  extend  in- 
definitely on  the  surface  of  the  cone  without  ever  coming 
together,  though  the  curves  would  approach  each  other 
for  ever.  Thus  the  parabola  is  the  limit  of  all  possible 
ellipses ;  for  it  is  manifest  that  as  the  cutting  plane 
becomes  more  and  more  nearly  parallel  to  the  side 
A  C,  the  axis  of  the  ellipse  cut  out  grows  longer  and 
longer,  and  just  at  the  point  where  parallelism  is  reached 
the  parabola  is  formed,  and  it  is  only  an  ellipse  with  an 
infinitely  elongated  axis. 

While  it  is  seen  that  the  branches  of  the  parabola  ap- 
proach each  other,  and  may  be  said  to  come  together  at 
an  infinite  distance  from  the  vertex  at  W,  this  is  not  the 
case  with  the  branches  of  the  hyperbola.*  Departing  from 
the  vertex  I,  and  passing  the  points  K  and  L,  the 
branches  of  the  hyperbola  recede  from  each  other  for 
ever,  losing  by  slow  degrees  their  curvature,  until  at  an 
infinite  distance  the  curves  degenerate  into  straight  lines, 
and  thus  continue  to  recede  for  ever.  Such  are  some  of 
the  general  characteristics  of  these  remarkable  curves. 
They  all,  like  the  ellipse,  have  a  major  axis,  on  each 
side  of  which  they  are  symmetrical.  They  all  have  at 


286  THE     COMETS. 

least  one  focus,  possessing  special  properties.  They  all 
have  a  vertex  lying  at  the  extremity  of  the  major  axis 
and  the  nearest  point  of  the  curve  to  the  focus ;  and, 
strange  as  it  may  seem,  in  either  one  of  these  curves 
mathematical  analysis  demonstrated  that  a  satellite  of 
the  sun  might  revolve  under  the  law  of  universal  gravita- 
tion. The  elliptic  orbits  of  the  planets  and  the  circular 
orbits  of  some  of  the  satellites  of  Jupiter  presented 
examples  in  the  heavens  of  two  of  these  curves,  and  it  oc- 
curred to  the  sagacious  mind  of  Newton  that  the  hitherto 
unexplained  eccentricity  of  the  cometary  revolutions 
might  be  accounted  for  by  finding  that  they  revolved 
around  the  sun  in  ellipses  of  great  eccentricity,  or  pos- 
sibly in  parabolic,  or  even  in  hyperbolic  orbits.  The 
English  astronomer  had  the  opportunity  of  putting  to 
the  test  this  grand  idea  by  the  appearance  of  a  great 
comet  in  1680,  which  displayed  a  train  of  light  of  won- 
derful dimensions  and  seemed  to  plunge  nearly  vertically 
downwards  from  the  pole  of  the  ecliptic,  made  its  peri- 
helion passage  with  almost  incredible  velocity,  and  with 
a  speed  always  diminishing  as  it  receded  from  the  sun 
again  swept  out  into  the  unfathomable  depths  of  space. 
To  this  comet  Newton  first  attempted  to  apply  the  law 
of  gravitation,  and  to  assign  it  an  orbit  among  the  conic 
sections.  This  could  be  done  in  the  same  manner  from 
observation  as  in  the  case  of  a  planet.  Having  obtained 
as  many  places  of  the  comet  as  possible  among  the  fixed 
stars,  it  remained  to  see  whether  any  elliptic  orbit  or 
any  parabolic  orbit  could  be  assigned  the  comet  which 
would  at  the  same  time  pass  through  all  these  observed 
places.  If  this  could  be  done,  then  it  would  become  pos- 
sible from  this  known  orbit  to  predict  the  places  of  a 
comet  as  of  a  planet,  and  in  the  event  of  the  orbit  prov- 


THE    COMETS.  287 

ing  elliptic,  then  the  return  of  the  comet  to  its  perihelion 
might  be  computed  and  announced. 

The  comet  of  1680  was  carefully  studied  by  Newton, 
and  its  orbit  was  found  to  be  an  extremely  elongated 
ellipse,  approaching  very  nearly  to  the  form  of  a  para- 
bola, but  while  its  physical  features  and  its  near  approach 
to  the  sun  made  it  an  object  of  extraordinary  interest,  the 
exceeding  velocity  with  which  it  swept  around  the  sun 
rendered  it  difficult  to  execute  exact  observations,  and 
hence  this  comet  was  not  well  adapted  to  demonstrate  the 
truth  of  the  rigorous  application  of  the  law  of  gravitation 
to  the  orbital  movements  of  these  eccentric  bodies. 
Another  great  comet  appeared  two  years  later,  in  1682, 
to  whose  history  there  attaches  a  special  interest,  on 
account  of  the  fact  that  it  was  the  first  of  these  bodies 
shown  to  have  a  permanent  orbit  in  connection  with  the 
solar  system,  and  the  first  whose  periodic  time  was 
sufficiently  well  computed  to  render  it  possible  to  predict 
its  return.  This  comet  bears  the  name  of  the  great 
English  astronomer  Halley,  to  whom  we  are  indebted  for 
the  computation  of  the  elements  of  its  orbit — a  problem, 
at  the  time  it  was  executed,  far  more  difficult  than  any 
belonging  to  the  whole  range  of  physical  astronomy. 

The  elements  of  the  orbit  of  a  comet  are  nearly  iden- 
tical with  those  which  fix  the  magnitude  and  position  of  a 
planetary  orbit.  To  obtain  the  magnitude  of  the  comet- 
ary  ellipse  we  must  have  two  elements,  the  length  of  the 
major  axis  and  the  perihelion  distance.  To  obtain  the 
direction  of  the  longer  axis  we  must  have  the  position  of 
the  perihelion  point ;  this  point,  being  joined  to  the  sun's 
center,  gives  the  direction  of  the  major  axis.  To  obtain 
the  position  of  the  plane  of  the  orbit  we  must  have  the 
place  of  the  ascending  or  descending  node,  and  also  the 


288  THE    COMETS. 

inclination  of  the  plane  of  the  cometary  orbit  to  that  of 
the  ecliptic.  If,  in  addition  to  these  elements,  we  have 
the  time  of  perihelion  passage,  then  it  becomes  possible 
to  follow  the  comet  in  its  erratic  movements  with  a  cer- 
tainty almost  as  great  as  that  with  which  the  orderly 
movements  of  the  planets  are  pursued. 

On  the  appearance  of  the  great  comet  of  1682,  Halley 
undertook  the  laborious  and  hitherto  unaccomplished  task 
of  computing  rigorously  the  elements  of  its  orbit,  which 
task  he  accomplished  after  incredible  labor  in  the  most 
masterly  manner.  It  then  occurred  to  him  to  gather  up 
all  historic  details  with  reference  to  the  appearance  of 
comets,  as  well  as  all  astronomical  observations,  so  that 
by  examination  and  inter-comparison  he  might  learn 
whether  any  recorded  comet  had  ever  pursued  the  same 
track  in  the  heavens  which  had  just  been  passed  over  by 
the  comet  of  1682.  In  the  course  of  this  historical  in- 
vestigation he  found  that  comets,  somewhat  resembling  in 
physical  appearance,  and  traversing  nearly  the  same 
regions  of  space  passed  over  by  his  own  comet,  had  ap- 
peared in  the  years  1531  and  1607,  and  now  again  in 
1682.  These  epochs  are  separated  by  an  interval  of 
between  seventy-five  and  seventy-six  years,  and  Halley, 
after  long  and  laborious  computation,  announced  that  in 
1759,  three  quarters  of  a  century  from  the  date  of  the 
prediction,  this  same  comet  would  again  return  to  our 
system  !  We  can  readily  sympathize  with  the  feelings 
of  this  great  astronomer  when  we  find  him  appealing  to 
posterity  to  remember,  in  the  event  of  his  prediction  being 
verified,  that  such  an  occurrence  as  the  return  of  a  comet 
was  first  announced  by  an  Englishman.  As  the  year 
1759  approached,  the  prophetic  declaration  of  Halley  ex- 
cited an  unusual  interest  throughout  the  astronomical 


THE    COMETS.  289 

world.  To  predict  the  exact  point  in  the  heavens  to 
which  the  telescope  must  be  directed  to  catch  the  first 
faint  glimpse  of  the  returning  stranger,  and  to  give  the 
date  of  its  perihelion  passage,  required  investigations  of 
so  high  an  order,  that  in  case  they  had  been  demanded  of 
Halley,  seventy-six  years  before,  the  then  existing  con- 
dition of  mathematical  and  physical  science  would  not 
have  furnished  the  means  for  their  accomplishment. 
The  whole  subject  of  planetary  perturbations  had  by  this 
time  been  tolerably  well  developed,  and  the  laborious 
task  of  computing  the  disturbing  influence  of  Jupiter  and 
Saturn  was  undertaken  by  Clairault,  assisted  by  La 
Lande  and  by  a  lady,  Madam  Lepaute,  whose  name  stands 
in  honorable  union  with  the  two  profound  mathematicians. 
After  many  months  of  indefatigable  labor  the  computers 
announced  that  for  want  of  time  they  had  been  compelled 
to  omit  several  matters  which  might  make  a  difference 
of  thirty  days,  one  way  or  the  other,  in  the  return  of  the 
comet,  but  that  within  these  limits  this  long  lost  celestial 
wanderer  would  pass  his  perihelion  on  the  1 3th  April, 
1759.  The  limits  of  error  were  justly  chosen,  for  the 
comet  actually  returned  and  passed  its  perihelion  on  the 
12th  of  March,  just  a  month  ahead  of  the  predicted  time. 
This  successful  computation  settled  for  ever  the  doc- 
trine of  the  cometary  orbits,  and  demonstrated  beyond 
doubt  their  subjection  to  the  attractive  power  of  the  sun, 
and  that  this  orb  extended  its  influence  into  the  profound 
depths  of  space,  to  which  the  comet  descended  during  its 
journey  of  seventy-six  years.  It  was  further  established 
that  Halley's  comet  was  a  permanent  member  of  the 
solar  system,  performing  its  orbital  revolution  around  the 
sun  in  an  exceedingly  elongated  ellipse,  but  with  a  regu- 
larity equal  to  that  of  the  planets.  It  was  further  de- 

13 


290  THE     COMETS. 

termined  that  the  entire  mass  of  the  comet  was  very  in- 
considerable, as  no  account  of  this  mass  was  made  in  the 
computations  for  perturbation,  while  the  masses  of  Jupi- 
ter and  Saturn  required  to  be  known  with  precision. 
This  comet  has  returned  a  second  time  since  its  discovery 
by  Halley,  when  its  elements  were  more  accurately  ob- 
tained by  many  modern  astronomers,  and  perhaps  best  of 
all  by  Hermann  Westphalen,  who  predicted  its  peri- 
helion passage,  after  an  absence  of  seventy-six  years,  to 
within  Jive  days  !  This  appearance  took  place  at  the 
close  of  1835.  We  shall  have  occasion  to  recur  to  this 
comet  again  when  we  come  to  speak  of  their  physical 
constitution. 

Westphalen  furnishes  the  following  as  the  actual  di- 
mensions of  Halley's  comet : — 

Perihelion  distance, 55,900,000  miles. 

Aphelion         " 3,370,300,000     " 

Length  of  the  major  axis,     ....  3,426,200,000     " 

Breadth  of  the  orbit, 826,900,000     " 

It  is  thus  seen  that  in  its  journey  from  the  sun  this 
comet  crosses  the  orbits  of  all  the  known  planets,  and 
passes  the  boundary  of  Neptune  more  than  three  hundred 
millions  of  miles. 

Having  thus  demonstrated  the  subordination  of  these 
extraordinary  bodies  to  the  law  of  universal  gravitation 
and  to  the  received  laws  of  motion,  we  will  proceed  to 
examine  their 

PHYSICAL  CONSTITUTION. — The  solid  earth  we  in- 
habit, the  moon,  her  satellite,  the  sun  and  all  the  planets, 
are  compact  masses  of  matter  of  differing  densities,  but 
of  firm,  compact  materials.  The  comets,  on  the  contrary, 
as  a  class,  seem  to  be  vaporous  masses,  far  more  unsub- 
stantial than  the  lightest  summer  cloud,  and  in  general 


THE    COMETS.  291 

transparent,  or  at  least  translucent,  even  in  their  most  con- 
densed portions.  This  is  evident  from  the  fact  that  the 
minute  stars  are  still  visible  with  undiminished  light 
when  seen  sometimes  through  a  depth  of  cometary  mat- 
ter millions  of  miles  in  extent.  Comets  in  general  con- 
sist of  a  nucleus  or  head,  the  center  of  force  and  the  most 
condensed  portion  of  their  matter.  Around  this  head 
there  is  seen  usually  a  vaporous  envelope  or  atmosphere 
of  greater  or  less  extent,  sometimes  evidently  divided 
into  concentric  layers  of  nearly  globular  form.  Many 
comets,  on  approaching  the  sun,  undergo  extraordinary 
physical  changes  in  the  head  or  nucleus,  which  experi- 
ences an  excessive  agitation,  flinging  out  jets  or  streams 
of  fiery  light  in  a  direction  towards  the  sun,  which  as- 
sume many  and  strange  forms,  sometimes  spreading  out 
into  a  fan-shaped  figure,  and  rapidly  fading  in  intensity, 
as  they  recede  from  the  nucleus.  This  phenomenon  is  al- 
most invariably  attended  or  followed  with  another  even 
more  remarkable — the  throwing  off  a  train  of  luminous 
matter,  called  the  tail,  in  a  direction  opposite  the  sun, 
and  sometimes  extending  to  a  prodigious  distance.  Thus 
the  tail  of  the  great  comet  of  1680,  already  mentioned, 
according  to  the  computations  of  Sir  Isaac  Newton, 
reached  to  a  distance  of  more  than  140  millions  of  miles, 
while  only  two  days  were  occupied  in  projecting  this  in- 
scrutable and  mysterious  appendage  to  this  enormous  dis- 
tance. The  form  of  the  tail  is  usually  that  of  a  hollow 
paraboloid,  the  nucleus  occupying  the  focus,  and  thus 
the  tail,  as  it  recedes  from  the  head,  seems  to  diverge 
into  two  streams  of  light,  while  the  axis  or  central  line  is 
comparatively  dark.  Sometimes,  as  in  the  great  comet 
of  1858,  the  region  immediately  behind  the  nucleus  on 
the  axis  is  jet  black — the  intensity  of  this  blackness 


292  THE     COMETS. 

growing  less  and  less  along  the  axis  until  it  finally  fades 
out  in  the  general  luminosity  of  the  tail. 

The  nucleus  is  sometimes  tolerably  well  defined,  and 
presents  a  planetary  disk  of  greater  or  less  magnitude. 
It  is  not  intended  to  assert  that  there  are  no  comets  which 
are  solid  bodies,  at  least  in  some  portion  of  their  central 
masses.  Indeed,  if  we  are  to  credit  the  records,  some 
have  been  seen  in  the  act  of  crossing  the  disk  of  the  sun, 
when  they  have  appeared  as  round,  well  defined,  circu- 
lar black  spots,  exactly  like  the  planets  Yenus  and  Mer- 
cury, when  seen  in  the  same  condition  on  the  bright  sur- 
face of  the  sun.  For  the  most  part,  however,  we  know 
that  these  bodies  do  not  present  any  evidence  of  solidity. 
Their  heads  or  nuclei  are  ill  defined  when  examined  by 
powerful  telescopes,  and  their  gaseous  condition  is  demon- 
strated by  the  fact  that  they  expand  and  contract  their 
dimensions  with  great  rapidity,  according  to  circum- 
stances. 

This  contraction  generally  takes  place  as  the  comet  ap- 
proaches its  perihelion  passage,  which  is  certainly  a  very 
curious  fact,  and  quite  contrary  to  what  we  would  expect, 
as  the  excessive  heat  to  which  a  comet  must  be  subjected 
in  perihelio  ought  (as  would  seem)  to  greatly  expand  its 
dimensions.  It  is  doubtless  owing  to  the  fact  that  this 
enormous  heat  extends  its  influence  so  far  that  the  vapor- 
ous mass  is  expanded  and  rarified  to  such  a  degree  as  to 
become  absolutely  transparent  and  invisible,  and  it  is  only 
when  released  from  this  intense  heat  by  recess  from  the 
sun  that  a  condensation  takes  place,  and  thus  the  seem- 
ing dimensions  of  the  comet  increases.  It  is  difficult  to 
comprehend  how  some  of  these  bodies,  in  their  nearest  ap- 
proach to  the  sun,  are  not  absolutely  burned  uj  and  dis- 
sipated for  ever.  The  great  comet  of  1680,  when  in 


THE    COMETS.  29S 

perihelio,  was  only  about  147,000  miles  distant  from  the 
sun's  surface ;  and  admitting  that  the  heat  of  the  sun 
diminishes  as  the  square  of  the  distance  increases,  Newton 
computed  that  the  comet  was  subjected  to  a  heat  2,000 
times  more  intense  than  that  of  red  hot  iron.  The  great 
comet  of  1843  is  computed  to  have  'approached  the  sun's 
surface  to  within  half  the  above  distance,  and  Sir  John 
Herschel  computes  that  the  intensity  of  the  heat  then  ex- 
perienced by  this  comet  was  47,000  times  greater  than 
the  heat  of  the  sun  as  received  at  the  earth,  or  more  than 
twenty-eight  times  greater  than  the  heat  concentrated  at 
the  focus  of  a  lens  of  thirty-two  inches  diameter,  which 
melted  agate  and  rock  crystal,  and  dissipated  these  re- 
fractory solids  into  an  invisible  gas  ! 

After  passing  under  the  influence  of  such  intense  heat, 
it  seems  almost  impossible  that  any  well  defined  form 
should  ever  be  recovered,  and  yet  the  comet  of  1680  and 
that  of  1843  finally  receded  from  the  sun,  the  nucleus 
in  some  mysterious  way  slowly  gathering  up  its  dis- 
persed particles  and  sweeping  away  into  the  dep'ths  of 
space,  a  well-defined  luminous  object,  not  in  any  sensible 
degree  injured  in  its  form  or  magnitude  by  this  fiery 
ordeal. 

The  envelopes  of  comets  and  their  tails  are  by  far  the 
most  inscrutable  problems  of  nature.  Of  these  pheno- 
mena no  satisfactory  account  has  yet  been  rendered. 
The  envelopes  of  the  comet  of  1858  were  beautiful  in 
form,  with  a  well  defined  circular  outline,  in  whose  center 
the  nucleus  blazed  with  its  fiery  light.  The  diameter  of 
this  seemingly  globular  mass  changed  from  night  to  night. 
Its  texture  varied;  sometimes  evenly  and  beautifully 
shaded  and  gauze-like  in  its  surface,  and  sometimes  this 
gauzy  surface  broken  by  dark  and  irregular  patches.  A 


294  THE    COMETS. 

second  concentric  sphere  became  visible,  fainter  in  its 
outline  than  the  interior  one,  and  finally  a  third  circle 
dimly  presented  its  outline,  very  faint,  and  only  to  be 
seen  in  powerful  telescopes,  under  favorable  circum- 
stances. 

The  beautiful  forms  exhibited  in  these  envelopes  and 
retained  by  them  seems  to  demonstrate  the  existence  of 
some  central  repulsive  force  located  in  the  nucleus,  and 
capable  of  holding  these  gaseous  particles  in  equilibrium. 
What  this  force  may  be  it  is  vain  to  conjecture.  If  the 
envelope  of  the  nucleus  is  a  phenomenon  surpassing  the 
reach  of  human  thought,  what  shall  we  say  of  the  still 
more  mysterious  and  incomprehensible  phenomena  pre- 
sented in  the  tails  of  comets  ? 

We  have  already  said  that  these  tails  are  thrown  off  in 
a  direction  opposite  the  sun  as  the  comet  approaches  its 
perihelion  passage.  As  the  comet  sweeps  around  the  sun 
with  almost  inconceivable  velocity,  the  tail  retains  its  di- 
rection, just  as  though  its  axis  were  a  solid  bar  of  iron, 
passing  through  the  nucleus  to  the  sun  and  hanging  on 
the  center  of  the  solar  orb.  This  bar,  extending  out  to 
the  furthest  extremity  of  the  tail,  sometimes  120  millions 
of  miles  beyond  the  nucleus,  sweeps  round  angularly  with 
equal  rapidity  at  every  point,  so  that  its  rectilinear  figure 
is  preserved  in  this  tremendous  sweep.  In  case  the  tail 
were  composed  of  ponderable  particles,  obedient  to  the 
laws  of  gravitation  and  motion,  this  would  be  impossible, 
for  if  we  consider  each  particle  an  independent  body,  de- 
scribing an  elliptic  or  parabolic  orbit  abou*  the  sun, 
the  laws  of  their  motion  would  compel  the  more  distant 
particles  to  lag  behind  the  nearer  ones  in  angular 
velocity. 

If  no  comet  ever  exhibited  any  other  than  this  peculiar 


THE  GREAT  COMET    OF  1858. 
KNOWN   AS"DONATl'S    COMET 


THE    COMETS.  295 

form  of  tail,  straight  and  directed  from  the  sun,  we 
might  frame  an  hypothesis  which  could  account  for  the 
facts ;  hut  in  some  instances  there  are  many  tails  to  the 
one  nucleus,  and  these  not  straight,  hut  curved  like  a 
cimetar.  In  other  cases  there  are  two  tails,  the  one,  as 
usual,  directed  from  the  sun,  the  other  pointing  towards 
the  source  of  light.  Sometimes  the  principal  tail  is 
straight,  and  in  the  direction  from  the  sun,  while  a  lateral 
ray  shooting  from  the  nucleus  may  form  with  the  axis  of 
the  tail  an  angle  of  thirty  or  even  sixty  degrees. 

We  have  already  said  that  the  tail  swings  around  the 
sun  in  the  perihelion  passage,  preserving  its  form  and  di- 
rection, and  hence,  when  the  comet  is  receding  from  the 
sun,  the  tail,  in  all  its  vast  dimensions,  is  driven  before 
the  head  of  the  comet,  preceding  the  nucleus  as  it  sweeps 
outward  into  space. 

In  some  instances  corruscations  have  been  noticed  to 
take  place  in  these  grand  but  mysterious  appendages, 
darting  with  incredible  velocity  from  the  very  nucleus  to 
the  extremity  of  the  tail,  and  thus  flashing  backwards 
and  forwards  like  a  magnificent  auroral  display. 

The  question  arises,  What  are  these  luminous  dis- 
plays ?  Are  the  tails  of  comets  composed  of  ponderable 
matter  ?  If  so,  do  they  yield  obedience  to  the  known 
laws  of  motion  and  gravitation  ?  Is  there  any  matter  in 
the  universe  which  may  ever  become  luminous,  but  is  im- 
ponderable ?  Can  these  tails  be  a  mere  effect  produced 
on  the  waves  of  light  emitted  by  the  sun  in  passing 
through  the  mass  of  cometary  matter  ?  These  and  many 
other  questions  equally  difficult  present  themselves  in 
this  connection.  The  re-absorption  of  the  tail  into  the 
head  would  seem  to  demonstrate  that  the  matter  compos- 
ing the  tail  was  ponderable,  while  the  facts  already  stated 


296  THE     COMETS. 

as  to  the  rigid  form  preserved  by  the  tail  in  sweeping 
around  the  sun  positively  contradicts  this  hypothesis. 

One  thing  we  know :  cometary  matter  is  ponderable 
matter,  and  obeys  the  laws  of  motion  and  gravitation,  is 
swayed  by  the  sun  and  by  the  planets,  and  in  all  par- 
ticulars complies  with  the  laws  governing  other  ponder- 
able matter.  This  we  know,  because,  as  we  have  seen, 
it  is  possible  to  predict  the  return  of  a  comet  revolving 
even  in  so  great  a  period  as  seventy-five  years,  and  such 
predictions  have  been  rigorously  verified.  In  case  any 
portion  of  this  ponderable  matter  were  absorbed  in  the 
sun,  or  dissipated  by  the  intense  heat  which  it  suffers  in 
the  perihelion  passage,  then  would  the  mass  of  the  comet 
grow  less  at  each  return,  and  the  periodic  time  would 
slowly  diminish.  There  is  one  comet,  named  after  its 
illustrious  discoverer,  Encke,  whose  history  for  the  past 
thirty  years  has  been  followed  with  high  interest,  be- 
cause it  is  now  a  fixed  truth  that  at  each  return  its  peri- 
helion passage  is  accelerated  by  about  two  and  a  half 
^  hours.  It  revolves  in  an  elliptical  orbit  of  small  dimen- 
sions comparatively,  and  performs  its  revolution  around 
the  sun  in  a  period  of  only  1,205  days,  or  about  three 
and  a  third  years.  By  assuming  the  existence  of  a  rare 
resisting  medium,  Professor  Encke  has  succeeded  in  ac- 
counting for  the  acceleration  in  the  motion  of  these 
comets,  and  this  hypothesis  has  been  generally  received. 
In  case  its  truth  becomes  established  it  involves  remote 
consequences  from  which  the  mind  naturally  revolts ;  for 
if  there  be  a  medium  capable  of  destroying  any  portion 
of  the  velocity  of  Encke' s  comet,  the  same  resistance 
must  in  like  manner  destroy  a  part  of  the  orbital  velocity 
of  every  planet  and  satellite,  and  sooner  or  later  each  in 
its  turn  must  by  slow  degrees  approach  the  sun,  and  in 


THE    COMETS.  297 

the  end  this  grand  central  orb  must  become  the  grave 
of  every  planet  and  satellite  and  comet  1  Such  an  hypo- 
thesis is  combatted,  possibly  disproved,  by  the  fact  that 
its  influence  has  not  yet  been  discovered  on  any  one  of 
the  planets  or  on  any  satellite.  It  may  be  argued  that 
on  these  solid  substantial  bodies  it  would  require  ages  to 
produce  sensible  effect,  while  on  the  vaporous  ethereal 
mass  of  Encke's  comet  even  an  almost  evanescent  medium 
might  produce  a  sensible  effect,  even  in  a  single  revolu- 
tion of  1,205  days.  May  it  not  be  possible  to  account 
for  the  decrease  of  the  periodic  time  of  Encke's  comet 
without  having  resort  to  an  hypothesis  involving  the 
destruction  of  the  entire  universe  ?  In  case  we  admit 
that  it  loses  a  portion  of  its  ponderable  matter  at  each 
perihelion  passage,  then  there  must  result  an  effect  like 
the  one  observed,  the  comet  slowly  approaching  the  sun, 
to  be  dissipated  entirely,  however,  before  absolutely  fall- 
ing on  the  surface  of  the  central  orb. 

However,  it  is  useless  to  speculate.  The  facts  now 
in  our  possession  are  not  sufficient  to  enable  us  to  render 
a  satisfactory  account  of  the  various  phenomena  iu  the 
physical  constitution  of  these  bodies  which  have  been 
enumerated,  and  we  can  only  hope  that  the  diligence 
and  pertinacity  with  which  this  branch  of  astronomy  ia 
now  pursued,  may  before  long  eventuate  in  removing 
from  the  science  this  only  source  of  doubt  and  uncer- 
tainty. 

In  the  meanwhile  the  conclusions  reached  by  Sir  John 
Herschel,  from  an  extended  and  careful  observation  of 
all  the  phenomena  presented  by  Halley's  comet  in  1835. 
6,  have  been  strengthened  by  the  facts  recorded  both  in 
Europe  and  America  of  the  great  comet  of  1848.  All 
the  observations  go  to  demonstrate — 

13* 


298  THE    COMETS. 

1.  That  the  surface  of  the  nucleus  nearest  the  sun 
becomes  powerfully  agitated,  and  finally  bursts  forth  into 
luminous  jets  of  gaseous  matter. 

2.  That  this  matter,  with  an  initial  velocity  driving  it 
towards  the  sun,  is  by  some  unknown  repelling  force 
driven  backwards  from  the  sun,  and  drifted  outward  from 
the  sun  to  vast  distances  forming  the  tail. 

3.  That  a  portion  of  this  vaporized  material  is  not 
subject  to  this  repulsive  force,  but  remains  under  the  in- 
fluence of  some  equally  inscrutable  central  power  lodged 
in  the  center  of  the  nucleus,  and  forming  the  corona  or 
envelope,   and  assuming  forms   of  great   delicacy  and 
beauty. 

4.  That  the  force  which  ejects  the  tail  cannot  be  gravi- 
tation, as  it  acts  with  a  power  and  in  a  direction  opposed 
to  this  central  power. 

5.  That  the  power  lodged  in  the  nucleus,  and  by  whose 
energy  the  particles   composing  the  tail  are  again  re- 
absorbed  into  the  head,  cannot  be  gravitation,  as  the 
minute  mass  of  the  comet  could  not  by  its  gravitating 
power  bring  back  the  particles  flung  off  to  such  enormous 
distances. 

In  this  catalogue  of  inscrutable  phenomena  we  must 
place  the  remarkable  fact  of  the  splitting  up  of  a  comet 
into  two  distinct  portions.  A  comet  of  short  period,  known 
as  Biela's  comet,  revolving  in  about  six  and  three  quarter 
years,  was  recognized  as  early  as  1826,  as  a  permanent 
member  of  the  solar  system. 

This  comet,  at  its  appearance  in  1832,  excited  a  pro 
found  sensation,  in  consequence  of  the  prediction  that  it 
would  cross  the  earth? s  path,  thereby  creating  the  great- 
est alarm  among  the  ignorant  lest  this  crossing  might 
occasion  a  collision  between  the  comet  and  the  earth. 


THE     COMETS.  299 

The  prediction  was  verified,  but  while  the  comet  was  in 
the  act  of  crossing  the  earth's  track  or  orbit,  the  earth 
was  many  millions  of  miles  removed  from  this  special 
point  of  intersection. 

The  appearance  in  1846  was  again  rendered  memor- 
able by  the  strange  phenomenon  already  mentioned — the 
actual  severation  of  the  comet  into  two  bodies,  distinct 
and  separate,  each  cometary  in  its  appearance,  and  each 
alternately  preponderating  in  apparent  magnitude  and 
brilliancy.  These  two  comets  possessed  all  the  charac- 
teristics which  mark  these  anomalous  bodies.  Each  had 
its  nucleus,  its  envelope,  and  its  tail.  The  first  indica- 
tion of  a  separation  occurred  as  early  as  the  19th  Decem- 
ber, 1845.  By  the  middle  of  January,  1846,  the  sepa- 
ration was  complete,  and  was  well  observed  in  Europe 
and  America.  By  the  beginning  of  March  the  interval 
had  increased  to  a  maximum,  when  it  was  about  one-third 
as  great  as  the  apparent  diameter  of  the  moon.  From 
this  time  the  companion  comet  began  to  fade,  remaining 
faintly  visible  up  to  the  15th  March.  After  this  the  old 
comet  remained  single,  and  finally  disappeared. 

Here  we  have  phenomena  of  the  most  extraordinary 
character.  What  convulsion  could  have  split  this  nebu- 
lous mass  into  two  distinct  fragments  ?  What  wonderful 
power  could  have  occasioned  the  alternations  in  the  in- 
tensity of  their  light?  What  mysterious  bond  could 
have  united  these  severed  and  separated  bodies,  and 
caused  them  to  vibrate  about  their  common  center  of 
gravity  ?  Have  these  bodies  been  permanently  re-united  ? 
or  will  they  ever  appear  as  individual  and  independ- 
ent objects?  These  questions  it  is  now  impossible  to 
answer. 

THE  NUMBER  OF  COMETS  far  exceeds  that  of  the  ^v~ 


300  THE    COMETS. 

and  their  satellites,  and,  indeed,  judging  from  the  list  of 
recorded  comets,  and  taking  into  account  the  fact  that 
multitudes  of  these  bodies  must  escape  notice  entirely  by 
their  remaining  above  the  horizon  in  the  day  time,  we  are 
forced  to  the  conclusion  that  they  are  not  to  be  numbered 
by  hundreds  or  thousands,  but  probably  by  millions! 
They  seem  to  obey  no  law  as  to  the  inclination  of  theii 
orbits  or  lae  direction  of  their  motions.  Some  appear 
to  plunge  vertically  downwards  from  the  very  pole  of  the 
ecliptic,  while  others  rise  upward  from  below  this  plane 
in  a  direction  diametrically  opposite.  Their  planer  are 
inclined  under  all  angles,  and  their  perihelion  points  <*re 
at  all  distances  from  the  sun.  Some  revolve  in  orbits  »>f 
moderate  eccentricity,  while  others  sweep  away  into 
space  in  parabolic  or  even  in  hyperbolic  orbits,  new 
again  to  visit  our  system  unless  arrested  and  diverted 
from  their  path  by  some  disturbing  power.  The  mighty 
depths  to  which  some  of  these  bodies  penetrate  into  space, 
sweeping,  as  they  must,  vastly  beyond  the  boundary  of 
the  planetary  system,  would  excite  a  doubt  in  the  mind 
as  to  whether  there  might  be  room  enough  in  space 
for  the  undisturbed  revolution  of  these  wonderful  ob- 
jects. We  shall  see  hereafter  that  profound  investiga- 
tions have  answered  this  inquiry  and  dispelled  every 
doubt  as  to  the  grandeur  of  the  scale  on  which  the  uni- 
verse is  built. 

In  the  Appendix  will  be  found  the  elements  of  the 
orbits  of  such  comets  as  are  regarded  permanent  members 
of  the  solar  system. 

We  here  close  our  examination  of  the  various  classes 
of  attendants  on  the  solar  orb.  We  find  this  mighty  sys- 
tem of  revolving  worlds  composed  of  bodies  which  are 
diverse  in  their  physical  constitution,  some  more  dense 


THE     COMETS.  801 

and  solid  than  the  earth  on  which  we  dwell,  some  far 
more  rare  and  unsubstantial  than  the  atmosphere  we 
breathe — all  obedient  to  the  grand  controlling  power  of 
the  central  orb,  while  no  one  is  relieved  from  the  dis- 
turbing influence  of  every  other — a  vast  complicated 
display  of  celestial  mechanism,  whose  equilibrium  and 
stability  presents  the  grandest  problem  for  human  in- 
vestigation to  be  found  in  the  whole  universe  of  matter. 


CHAPTER*  XV. 

THE  SUN  AND  PLANETS  AS  PONDERABLE  BODIES. 


GENERAL  CIRCUMSTANCES  OF  THE  SYSTEM. — THE  SUN. — His  DIAMETER  AND 
MASS. — GRAVITY  AT  THE  SURFACE. — MERCURY. — His  MASS  AND  PERTURBA- 
TIONS.— VENUS  AS  A  PONDERABLE  BODY. — LONG  EQUATION  OF  VENUS  ANE 
THE  EARTH. — THE  EARTH  AND  MOON  AS  HEAVY  BODIES. — FIGURE  AND 
MASS  OF  THE  EARTH. — PRECESSION. — ABERRATION. — NUTATION. — MARS. — 
His  MASS  AND  DENSITY.— GRAVITY  AT  His  SURFACE.— THE  ASTEROIDS.— 
JUPITER'S  SYSTEM.— SATURN.— His  MOONS  AND  KINGS  AS  PONDERABLE 
BODIES.— URANUS.— NEPTUNE.— STABILITY  OF  THE  WHOLE  SYSTEM. 


HAVING  now  completed  a  rapid  survey  of  the  bodies 
which  owe  allegiance  to  the  sun,  and  having  reached  to 
a  knowledge  of  those  laws  which  extend  their  empire  over 
all  these  revolving  planets,  we  come  to  the  considera- 
tion of  the  modifications  which  are  introduced  into  the 
circumstances  of  motion  of  each  of  these  worlds,  by  the 
fact  that  it  is  subjected  to  the  influence  of  all  the  others. 
As  under  the  great  law  of  universal  gravitation  every 
particle  of  matter  in  the  universe  attracts  every  other 
particle  of  matter  with  a  force  which  varies  inversely  as 
the  square  of  the  distance  and  directly  as  the  mass,  it 
follows  that  each  planet  and  comet  and  satellite  of  the 
entire  system  of  the  sun  are,  to  a  greater  or  less  degree, 
affected  by  the  attraction  of  every  other. 

We  have  already  considered  generally  the  great  pro- 
blem of  the  "  three  bodies" — a  central,  a  disturbing,  and 
a  disturbed  body.  The  train  of  reasoning  there  presented 


PONDERABLE     BODIES.  303 

is  now  to  be  carried  out  and  extended  in  succession  to  the 
planets  and  their  satellites.  Before  proceeding  to  ex- 
amine the  changes  wrought  in  the  orbits  of  the  planets 
and  their  satellites  by  the  action  of  all  the  disturbing 
forces,  we  will  make  a  more  general  examination  of  the 
various  elements  of  the  planetary  orbits,  to  learn,  if  pos- 
sible, whether  any  of  these  elements  are  subjected  to 
changes  which  are  merely  periodic  in  their  character,  re- 
turning after  intervals,  longer  or  shorter,  to  their  normal 
condition,  to  repeat  the  same  changes  in  the  same  order 
for  ever.  We  desire  also  to  inquire  whether  any  of  the 
elements  are  subjected  to  perturbations  which  always  pro- 
gress in  the  same  direction,  and  if  so,  whether  these 
changes  in  any  way  involve  the  destruction  of  the  system 
as  such. 

This  is  undoubtedly  the  grandest  problem  ever  pro- 
pounded to  the  human  mind,  for  it  is  neither  more  nor 
less  than  an  inquiry  into  the  perpetuity  of  the  great 
scheme  of  worlds  dependent  on  the  sun.  It  demands 
a  vision  which  shall  penetrate  the  future  ages  to  pre- 
dict the  mutations  and  their  effects  at  the  end  of  these 
ages.  It  will  not  be  expected  that  in  such  a  treatise  at 
this  we  are  to  enter  into  an  exhaustive  discussion  of  this 
great  subject.  We  can  do  little  more  than  announce  the 
results  reached  by  the  profound  investigations  of  the  great 
mathematical  successors  of  Newton. 

We  shall  commence,  then,  by  an  inquiry  touching 
those  elements  of  an  orbit  which  involve  the  well-being 
of  a  planet,  or  its  fitness  to  sustain  the  animal  and  vege- 
table life  which  exists  on  its  surface. 

The  figure  and  magnitude  of  an  orbit  are  determined 
by  the  length  of  the  major  axis  and  by  the  eccentricity r, 
and  in  case  but  one  planet  existed,  these  are  the  only 


804  THE    SUN    AND     PLANETS 

elements  whose  value  could  in  any  way  affect  the  physical 
condition  of  the  planet,  so  far  as  its  supply  of  light  and 
heat  received  from  the  sun  are  concerned.  In  this  case 
the  position  of  the  orbit  in  its  own  plane  (determined  by 
the  place  of  the  perihelion  point)  and  also  the  position 
of  the  plane  of  the  orbit,  as  referred  to  any  fixed  plane, 
(determined  by  the  angle  of  inclination  and  line  of 
nodes),  and  also  the  epoch  (or  place  of  the  planet  in  its 
orbit  at  a  given  moment  of  time),  all  those  quantities 
would  not  in  any  degree  affect  the  actual  condition  of  the 
planet ;  but  as  no  planet  is  isolated,  and  as  each  is  sub- 
jected to  the  influence  of  every  other,  it  becomes  a  mat- 
ter of  grave  importance  to  ascertain  whether  there  be  any 
fluctuations  in  the  values  of  all  these  elements,  whether 
these  fluctuations  are  confined  within  any  specific  limits, 
and  whether,  if  thus  confined,  any  injurious  effect  can 
result  to  those  elements  which  involve  the  well-being  of 
any  planet ;  and  finally,  whether  there  be  any  guarantee 
for  the  perpetuity  of  the  planetary  system  in  the  condi- 
tion now  existent. 

In  case  the  planes  of  the  orbits  of  all  the  planets  were 
coincident,  then  the  investigations  would  be  confined  to 
the  fluctuation  in  the  values  of  the  major  axes,  eccen- 
tricities and  perihelia;  but  from  the  reasoning  already 
presented  in  the  problem  of  "  the  three  bodies,"  we  have 
seen  that  if  we  consider  the  relation  of  two  planets  whose 
orbits  are  inclined  under  any  angle,  in  their  reciprocal 
influence,  if  we  assume  the  plane  of  the  orbit  of  one  of 
these  planets,  for  example,  the  earth,  as  fixed  in  position, 
and  the  plane  of  the  other  planet's  orbit  (as  Mars)  as  in- 
clined to  this,  under  a  given  angle,  it  is  clearly  manifest 
that  the  disturbing  influence  of  the  earth  on  Mars  will  be 
reversed  when  Mars  passes  through  the  plane  of  th« 


POND  E 


305 


earth's  orbit  Suppose  we  could  place  our  "eye  in  the 
prolongation  of  the  line  of  intersection  of  the  two  orbits, 
then  we  should  see  them  as  two  straight  lines,  inclined  to 
each  other,  as  in  the  figure  below,  in  which  S  represents 

-M 


the  place  of  the  sun,  E  E'  places  of  the  earth,  and  M  and 
M'  places  of  Mars.  Now,  when  Mars  and  the  earth  are 
on  the  same  side  of  the  sun,  or  the  line  of  nodes,  Mars 
ascending  towards  M',  above  the  plane  of  the  earth's 
orbit,  the  force  exerted  by  the  earth  on  the  ascending 
planet  tends  to  draw  it  downward  to  the  ecliptic,  and 
hence  it  will  not  quite  reach  the  elevation  M',  and  thus 
all  this  while  the  plane  of  the  orbit  of  Mars  will  be  form- 
ing a  less  and  less  angle  with  the  ecliptic.  The  moment, 
however,  the  planet  reaches  its  highest  elevation  and 
commences  to  descend  towards  the  ecliptic  to  pass  its  de- 
scending node,  then  the  earth,  remaining  stationary,  will 
pull  the  planet  towards  its  own  plane,  and  hence  the  de- 
scent will  be  made  steeper,  and  the  angle  of  inclination 
of  the  orbit  of  Mars  will,  while  the  planet  thus  descends, 
be  always  increasing.  Following  Mars  below  the  plane 
of  the  ecliptic,  the  earth  remaining  as  before,  we  see  that 
here  the  tendency  is  to  pull  Mars  up  to  the  earth's  orbit, 


306  THE    SUN    AND    PLANETS 

and  hence  it  will  not  quite  reach  the  point  M,  or  the  in- 
clination in  this  descent  below  the  ecliptic  will  diminish. 
From  this  point,  as  Mars  begins  to  ascend,  the  earth's  at- 
tractive energy  will  cause  it  to  ascend  more  rapidly,  and 
will  make  it  pass  its  ascending  node  earlier  than  if  un- 
disturbed, and  as  it  comes  up  faster,  it  must  ascend  a 
steeper  grade,  or  the  inclination  will  increase.  Thus  we 
see  that  Mars,  in  ascending  or  descending  to  pass  either 
node,  will  both  ascend  and  descend  by  a  steeper  grade 
because  of  the  earth's  attraction,  while  in  passing  from 
either  node  to  the  highest  and  lowest  points  of  its  orbit 
the  same  force  will  operate  to  make  the  planet  reach 
points  less  remote  from  the  ecliptic  than  if  undisturbed, 
and  hence  to  ascend  and  descend  with  a  smaller  angle  of 
inclination.  Now,  a  careful  inspection  will  show  that  the 
effects  produced  by  the  earth  on  Mars,  while  situated  at 
E',  will  be  greater  in  the  half  of  the  orbit  of  Mars  which 
lies  above  the  ecliptic,  and  at  the  end  of  one  revolution  an 
exact  compensation  may  not  be  effected,  so  that  the  in- 
crease of  the  angle  of  inclination  may  not  be  exactly 
equal  to  the  decrease.  But  as  the  earth  is  revolving,  a 
time  will  come  when  this  body  will  occupy  the  point  E, 
and  then  the  most  powerful  effect  will  be  produced  when 
Mars  is  below  the  ecliptic,  and  in  case  the  orbits  are 
circular,  an  exact  symmetry  existing,  at  the  end  of  a  cer- 
tain cycle  the  inclinations  will  be  exactly  restored. 

The  fact  that  the  orbits  of  the  planets  are  elliptical  in 
figure  cannot  in  any  way  lessen  the  force  of  the  reasoning 
we  have  employed  ;  it  can  only  postpone  to  a  more  remote 
period  the  final  restoration  of  the  inclinations  of  the 
planetary  orbits.  Under  the  powerful  and  masterly 
analysis  of  Lagrange  this  subject  was  completely  ex- 
hausted, and  a  result  reached  which  in  the  following  pro- 


AS    PONDERABLE    BODIES.  307 

position  guarantees  the  stability  of  the  inclinations  through 
all  ages : — 

"  If  the  mass  or  weight  of  every  planet  be  multiplied 
by  the  square  root  of  its  major  axis,  and  this  product  be 
multiplied  by  the  tangent  of  the  angle  of  inclination  of 
the  plane  of  the  planetary  orbit  to  a  fixed  plane,  and  these 
products  be  added  together,  their  sum  will  be  constantly 
the  same." 

Now,  we  will  show  hereafter  that  the  major  axes  re- 
main nearly  invariable,  the  masses  of  the  planets  are  ab- 
solutely so,  and  hence  the  third  factor  of  the  product,  the 
tangent  of  the  inclination,  can  only  vary  within  narrow 
limits,  returning  at  the  end  of  a  vast  cycle  to  the  primi- 
tive value. 

We  shall  see  hereafter  how  important  the  stability  of 
the  inclination  of  the  earth's  orbit  is  to  the  well-being 
of  the  living  and  sentient  beings  now  on  the  earth's 
surface. 

We  proceed  to  examine  the  changes  of  the  lines  of 
nodes  due  to  perturbation.  These  changes  are  allied  to 
those  of  inclination,  and  are,  indeed,  a  necessary  conse- 
quence of  these  changes,  as  may  readily  be  shown. 


308  THE    SUN    AND    PLANETS 

For  this  purpose  we  return  to  the  figure  already  em- 
ployed, using  the  same  planets,  Mars  and  the  earth,  re- 
garding the  movements  of  Mars  to  be  disturbed  by  the 
earth's  attraction. 

We  have  already  seen  that  in  case  Mars  be  at  M,  the 
earth  being  at  E,  the  planet,  in  descending  its  orbit  to 
the  line  of  nodes  seen  as  in  S,  (the  eye  of  the  spectator 
being  in  the  prolongation  of  the  line  of  nodes)  during  the 
entire  descent  the  planet  will  be  drawn  down  to  the  plane 
of  the  ecliptic  E  E'  on  a  steeper  grade  than  the  normal 
one  M  S,  and  hence  the  planet  will  pass  through  the 
ecliptic  earlier  than  if  undisturbed,  or  at  a  point  which 
will  be  seen  somewhere  between  S  and  E.  Thus  dur- 
ing this  descent  the  node  will  go  backwards  to  meet  the 
planet,  or  will  retrograde.  Passing  below  the  ecliptic, 
the  planet  continuing  to  descend,  will,  as  we  have  seen, 
be  prevented  by  the  disturbing  body  from  reaching  a 
point  so  low  as  M',  and  hence  if  its  path  for  a  moment 
were  anywhere  produced  backwards,  this  line  would  meet 
the  ecliptic  at  some  point  always  .approaching  E,  or  here 
again  the  line  of  nodes  retrogrades.  The  same  reasoning 
will  show  that  with  the  above  configuration  the  retro- 
gradation  of  the  line  of  nodes  must  continue  with  unequal 
velocity  during  the  entire  revolution  of  the  planet.  In 
other  configurations  there  is  sometimes  an  advance  of  the 
node,  but  in  the  long  run  it  is  easily  demonstrated  that 
the  nodes  of  all  the  planetary  orbits  on  any  fixed  plane 
will  retrograde  and  perform  entire  revolutions  in  periods 
of  greater  or  less  duration. 

This  perpetual  recess  of  the  lines  of  nodes  in  one  direc- 
tion does  not  in  any  way  affect  the  physical  condition  of 
a  planet,  but  serves  an  admirable  and  necessary  purpose 
in  securing  final  stability  in  the  planetary  system  by 


AS    PONDERABLE    BODIES.  809 

presenting  the  disturbed  orbits  to  the  disturbing  bodies 
under  all  possible  configurations. 

We  shall  not  attempt  to  exhibit  in  full  the  reasoning 
by  which  the  variations  of  the  remaining  elements  are 
shown  to  be  periodic,  when  periodicity  is  essential  to 
stability,  or  progressive  when  progression  does  not  in- 
volve destruction,  but  from  a  single  figure  deduce,  if  pos- 
sible, the  great  principles  involved  in  this  wonderful 
problem. 


Let  S  represent  the  sun,  E  the  earth,  and  P  any 
planet  disturbed  by  the  earth,  and  let  us  suppose  that  un- 
disturbed in  any  small  portion  of  time  it  would  reach  P', 
but  subjected  to  the  influence  of  the  earth's  attraction  it 
reaches  P"  in  the  same  time.  The  question  is,  in  what 
way  does  this  change  affect  the  elements  of  P's  orbit  ? 

We  have  already  seen  the  effect  on  the  inclination  and 
line  of  nodes.  These  elements  do  not  affect  the  magni- 
tude of  the  orbit  nor  the  position  of  that  orbit  in  its  own 
plane.  The  magnitude  and  position  depend  on  the  length 
of  the  major  axis,  eccentricity  and  perihelion  point  Let 
us  examine  these  in  order,  commencing  vith  the  length 
of  the  major  axis. 


310  THE    SUN    AND    PLANETS 

We  suppose  the  planet  P  to  be  moving,  when  undis- 
turbed, with  its  normal  elliptic  velocity,  and  of  course  on 
reaching  P',  the  longer  axis  of  its  orbit,  and  in  fact  all 
the  elements  remain  unchanged  in  value  ;  but  being  dis- 
turbed, so  as  to  be  prevented  from  reaching  P',  and  being 
compelled  to  reach  P",  "will  this  compulsion  merely 
change  the  position  of  the  planetary  orbit,  or  will  it  in- 
crease or  decrease  the  length  of  the  major  axis? 

Kepler's  third  law  tells  us  that  the  squares  of  the 
periodic  times  are  proportional  to  the  cubes  of  the  major 
axes,  and  from  this  relation  it  is  manifest  that  any  change 
in  the  elliptic  velocity  of  a  planet  must  change  the  period 
of  its  revolution,  and  this  involves  a  change  by  neces- 
sity in  the  major  axis  of  the  orbit. 

The  question  of  change  in  the  major  axis,  then,  re- 
solves itself  into  an  inquiry  as  to  whether  the  disturbance 
has  produced  any  change  in  the  elliptic  velocity  of  the 
disturbed  planet. 

At  the  first  glance  it  may  seem  impossible  to  drag  a 
planet  from  its  normal  elliptic  path  without  affecting  its 
velocity.  This,  however,  is  not  the  fact.  If  a  body  be 
moving  in  a  straight  line  and  a  force  be  applied  to  it 
perpendicular  to  the  direction  of  its  motion,  this  force 
will  not  in  any  degree  affect  the  velocity,  but  only  the 
direction  of  the  moving  body.  Thus  a  ball  fired  from  a 
rifle  on  the  deck  of  a  fixed  or  moving  boat,  with  the  same 
initial  force,  will  reach  the  opposite  shore  in  the  same 
time,  but  its  direction  of  absolute  motion  is  changed  if 
fired  from  a  moving  boat,  from  what  it  would  be  if  shot 
from  one  at  rest.  So  a  flying  planet  may  be  subjected 
to  the  action  of  a  force  always  perpendicular  to  the  di- 
rection of  its  motion,  which  force  may  push  it  from  its 
normal  path,  but  cannot  affect  its  elliptical  velocity. 


AS    PONDERABLE     BODIES. 


311 


Such  a  force,  then,  can  have  no  influence  on  the  length 
of  the  major  axis,  or  on  the  periodic  time  of  the  re- 
volving body. 

Now,  every  force  is  capable  of  being  changed  into  three 
other  forces  whose  combined  action  will  produce  the  samo 
effect  as  the  primitive  force,  as  in  the  figure. 


Let  J?  P""  represent  the  direction  and  intensity  of  any 
force ;  on  this  line  as  a  diagonal  construct  the  solid 
figure  a  parallelepiped.  Then  the  sides  P  P',  P  P"  and 
P  Y"  will  represent  the  direction  and  intensity  of  three 
forces,  which  would  produce  the  same  effect  as  the  force 
P  P'"'. 

Precisely  in  this  way  the  disturbing  force  exerted  by 
the  earth  on  the  planet  P  can  be  converted  into  three 
other  forces,  whose  combined  effect  shall  be  identical  with 
the  original  force.  Two  of  these  forces  shall  lie  in  the 
plane  of  the  planet's  motion,  the  one  tangent  to -the 
orbit,  or  in  the  exact  direction  of  the  planet's  motion, 
the  second  perpendicular  to  the  direction  of  motion,  or 
normal  to  the  orbit,  and  the  third  perpendicular  to  the 
plane  of  the  orbit  of  the  planet. 

Now,  from  what  we  have  said,  it  is  clear  that  but  one 


812  THE    SUN    AND     PLANETS 

of  these  new  or  substituted  forces  can  in  any  way  affect 
the  velocity  of  the  planet,  and  that  is  the  force  tangent 
to  the  orbit,  or  coincident  with  the  direction  in  which  it 
is  moving.  The  normal  component  (as  it  is  called) 
pushes  the  planet  from  its  old  orbit  and  the  perpendicu- 
lar component  pushes  the  planet  above  or  below  its  own 
plane  of  motion,  but  neither  of  these  affect  the  velocity 
of  the  moving  planet,  and  neither  of  them  can  in  any  de- 
gree affect  the  length  of  the  major  axis. 

The  perpendicular  component  has  already  been  con- 
sidered in  its  effects,  for  it  is  this  force  which  changes  the 
inclination  and  gives  motion  to  the  line  of  nodes.  We 
may,  therefore,  in  our  future  examinations  leave  this 
force  out  of  consideration,  or,  which  comes  to  the  same 
thing,  consider  the  planes  of  the  orbits  of  the  disturbing 
and  the  disturbed  planet  as  the  same. 

Let  us,  then,  represent  by  the  two  circles  the  orbits 
of  the  planets  in  question,  S  being  the  place  of  the  sun, 


E  the  earth,  and  P  the  planet  when  in  conjunction.  In 
this  configuration  the  entire  disturbing  power  of  E  is 
exerted  along  the  line  E  P,  or  perpendicular  to  the  direc- 
tion of  the  planet's  motion,  or  normal  to  its  orbit,  and  in 


AS    PONDERABLE     BODIES.  318 

this  position  the  tangential  force  being  nothing,  the  major 
axis  is  undisturbed  by  E.  As  P  moves  towards  P'  the 
direction  of  the  force  exerted  by  E  ceases  to  be  normal  to 
P's  orbit,  and  may  be  replaced  by  a  normal  and  a  tan- 
gential force.  The  tangential  force  from  P  towards  P' 
is  manifestly  in  opposition  to  the  motion  of  P  in  its  orbit, 
and  therefore  retards  its  motion,  and  thus  decreases  its 
major  axis ;  but  there  is  a  point  P"  symmetrically  placed 
with  reference  to  P,  where  the  tangential  force  is  in  the 
opposite  direction,  and  in  an  equal  degree  becomes  an 
accelerating  force,  and  whatever  the  major  axis  might 
lose  in  length  from  the  disturbing  power  at  P',  it  would 
gain  from  the  same  power  when  it  comes  to  occupy  the 
point  P".  So  that  if  E  should  remain  fixed  during  an 
entire  revolution  of  P,  a  compensation  would  be  effected, 
and  the  velocity  of  the  planet  on  reaching  its  point  of 
departure  would  be  identical  with  that  with  which  it 
started,  and  hence  the  major  axis,  though  it  would  have 
lost  and  gained,  would  in  the  end  be  restored  to  its 
primitive  value. 

If  the  orbits  were  elliptical  and  their  major  axes  were 
coincident  the  same  reasoning  from  symmetry  would  still 
hold  good,  and  demonstrate  the  restoration  of  the  major 
axis,  and  as  action  and  reaction  are  always  equal,  it  is 
manifest  that  by  fixing  P  and  causing  E  to  revolve,  the 
changes  wrought  by  E  on  P  would  now  be  wrought  by 
P  on  E,  only  in  the  reverse  order — that  is,  wherever  P 
was  accelerated  by  E,  E  will  be  retarded  by  P,  and  vice 
versa. 

Admitting  the  major  axes  to  be  inclined  to  each  other 
destroys  the  symmetry  of  the  figure,  and  an  exact  resto- 
ration is  not  effected  in  one  revolution  ;  but  as  the  peri- 
helia of  the  planetary  orbits  are  all  in  motion,  the  time 

14 


814  THE     SUN    AND     PLANETS 

•will  come  when  a  coincidence  of  the  major  axes  will  be 
effected,  and  if  there  be  a  certain  amount  of  outstanding 
uncompensated  velocity,  when  the  coincidence  takes  place, 
the  action  will  be  reversed,  and  at  the  end  of  one  grand 
revolution  of  the  major  axes  from  coincidence  to  coinci- 
dence the  restoration  will  be  completed,  and  the  axes  will 
return  to  their  primitive  value. 

Here  we  are  compelled  to  leave  the  problem,  and  simply 
state  the  result  which  a  complete  solution  has  effected. 
We  are  again  indebted  to  Lagrange  for  the  resolution  of 
this  most  important  of  all  the  problems  involving  the 
stability  of  the  solar  system,  who  presents  the  final  result 
as  follows  : — 

"  If  the  mass  of  each  planet  be  multiplied  by  the  square 
root  of  the  major  axis  of  its  orbit,  and  this  product  by  the 
square  of  the  tangent  of  the  inclination  of  the  orbit  to  a 
fixed  plane,  and  all  these  products  be  added  together, 
their  sum  will  be  constantly  the  same,  no  matter  what 
variations  exist  in  the  system." 

The  mass  or  weight  of  each  planet  is  invariable,  while 
the  loss  or  gain  in  the  values  of  the  major  axes  is  always 
counterpoised  by  the  gain  or  loss  in  the  inclination  of  the 
orbits,  and  thus  in  the  long  run,  in  cycles  of  vast  periods, 
a  complete  restoration  of  the  major  axes  is  fully  accom- 
plished, and  the  system  in  this  particular  returns  to  its 
normal  condition. 

We  have  thus  far  considered  the  effect  of  two  out  of 
the  three  forces  into  which  a  disturbing  force  may  be  de- 
composed. The  normal  component  remains  to  be  ex- 
amined. This  acts  in  a  direction  normal  to  the  curve 
described  by  the  planet,  or  perpendicular  to  the  tangent 
to  the  orbit  at  the  point  occupied  by  the  planet.  We 
shall  not  enter  into  any  extended  examination  of  this  sub- 


AS    PONDERABLE    BODIES.  315 

jectj  and  will  only  say  that  this  component  of  the  dis- 
turbing force  gives  rise  to  a  movement  in  the  perihelion 
points  of  the  planetary  orbits,  sometimes  advancing  these 
points,  sometimes  giving  them  a  retrograde  motion,  and 
in  some  instances  producing  oscillations. 

These  effects  are  necessarily  mixed  up  and  combined 
•with  those  produced  by  the  action  of  the  tangential  force, 
for,  as  we  have  seen,  the  effect  of  this  force  goes  to  in- 
crease or  decrease  the  value  of  the  major  axis ;  but  no 
increase  or  decrease  of  the  major  axis  can  take  place 
without  a  corresponding  change  in  the  eccentricity,  so 
that  these  changes  thus  modified,  the  one  by  the  other, 
finally  become  exceedingly  complex,  and  can  only  be 
traced  and  computed  by  the  application  of  the  highest 
powers  of  analytic  reasoning. 

The  complexity  is  further  increased  from  the  fact  that 
in  the  consideration  of  the  entire  problem  of  perturbations 
the  varying  distances  of  the  disturbing  arid  disturbed 
bodies  must  be  rigorously  taken  into  account,  and  may 
modify  and  even  reverse  the  effects  due  simply  to  direc- 
tion. With  difficulties  so  extraordinary  and  diversified, 
with  complications  and  complexities  mutually  extending 
to  each  other,  involving  movements  so  slow  as  to  re- 
quire ages  for  their  completion,  it  is  a  matter  of  amaze- 
ment that  the  human  mind  has  achieved  complete  success 
in  the  resolution  of  this  grand  problem,  and  can  with 
confidence  pronounce  the  changes  to  fall  within  narrow 
and  inocuous  limits,  while  in  the  end,  after  a  cycle  of 
incalculable  millions  of  years,  the  entire  system  of  planets 
and  satellites  shall  return  once  more  to  their  primitive 
condition,  to  start  again  on  their  endless  cycles  of  con- 
figuration and  change. 

There  remains  one  more  source  whence  arises  an  ac- 


316  THE    SUN    AND     PLANETS 

cumulation  of  disturbance,  progressive  in  the  same  direo 
tion  through  definite  cycles  of  greater  or  lesser  duration. 
I  mean  the  effects  due  to  a  near  commensur ability  of 
the  periods  of  revolution  of  the  disturbed  and  disturbing 
planets.  The  nearer  the  approach  to  commensurability 
the  longer  will  be  the  duration  of  the  resulting  in- 
equality. 

We  shall  have  occasion  to  resume  this  subject  in  our 
examination  of  the  circumstances  of  disturbance  belonging 
to  each  individual  planet,  which  we  shall  now  proceed 
to  examine  briefly,  commencing  at  the  sun,  and  proceed- 
ing outwards. 

THE   SUN    CONSIDERED   AS  A   GRAVITATING    BODY. — 

We  shall  now  return  to  the  great  center  of  the  planetary 
worlds  with  a  full  knowledge  of  the  laws  of  motion  and 
gravitation,  and  provided  with  the  instrumental  means 
of  securing  those  delicate  measures  whereby  the  solar  orb 
may  be  determined  in  distance,  volume  and  weight. 


B 


We  have  already  explained  how  these  quantities  may 
be  obtained,  and  we  now  present  the  results  of  exact 
measures  and  accurate  computation.  The  sun's  mean 
distance  from  the  earth  may  be  taken  at  ninety-five  mil- 
lions of  miles.  By  exact  measures  the  mean  diameter 
of  the  sun  subtends  an  angle  equal  to  32'.01//.8,  and  an 
angle  of  this  value  indicates  a  real  diameter  in  the  sun 
of  883,000  miles,  as  may  be  seen  from  the  figure  above, 


AS    PONDERABLE    BODIES.  317 

in  which  it  is  evident  that  a  line  A  B  subtends  at  A'  B', 
a  much  smaller  angle  than  when  located  at  A  B,  nearer 
the  vertex.  If,  then,  we  have  a  given  angle  A'  E  B', 
and  a  given  distance  E  B',  from  the  vertex,  if  we  erect 
the  line  B'  A!  it  is  evident  the  length  of  this  line  will 
be  determined  by  the  value  of  the  angle  B'  E  A'  and 
the  length  of  the  line  E  B' ;  so  the  sun's  distance  and 
angular  diameter  determines  his  real  diameter.  This 
diameter  of  the  sun  (88 i, 000  miles),  in  terms  of  the 
diameter  of  the  earth,  amounts  to  111.454,  and  as  the 
volumes  of  two  globes  are  in  the  proportion  of  the  cubes 
of  their  diameters,  we  shall  have" the  volume  of  the  sun 
to  the  volume  of  the  earth  as  (111.454)3  is  to  (1)  ,  or  as 
1,384,472  to  1,  or  it  would  require  no  less  than  one 
million  three  hundred  and  eighty-four  thousand  four 
hundred  and  seventy-two  globes  as  large  as  the  earth  to 
fill  the  vast  interior  of  a  hollow  sphere  as  large  as  the 
sun.  By  this  we  do  not  mean  to  assert  that  the  sun 
weighs  as  much  as  1.384,472  earths.  This  is  not  the 
fact  We  have  seen  already  the  process  by  which  the 
relative  weights  of  these  globes  may  be  reached,  and  we 
have  found  that  the  force  exerted  on  the  earth  by  the 
sun,  enfeebled  by  the  distance  at  which  it  acts,  and 
thus  reduced  to  the  160,000th  part  of  its  actual  value, 
at  a  distance  equal  to  that  of  the  moon,  still  exceeds 
in  a  more  than  twofold  ratio  the  force  exerted  by  the 
earth  on  the  moon ;  and  when  the  exact  ratio  is  applied 
we  find  the  weight  of  the  sun  to  be  equal  to  354,936 
earths,  and  this  is  what  we  call  the  mass  of  the  sun. 

If  we  divide  the  mass  by  the  volume  we  obtain  the 
specific  gravity  of  the  sun,  in  terms  of  that  of  the 
earth,  equal  to  T;VW  ffin= 0.2564— that  is,  the  aver- 
age weight  of  one  cubic  foot  of  the  sun  is  only  one-fourth 


318  THE    SUN     AND    PLANETS 

as  great  as  the  average  weight  of  one  cubic  foot  of  the 
earth. 

It  is  the  mass  of  the  sun  and  not  its  volume  which 
determines  the  amount  of  force  which  this  great  central 
globe  exerts.  Its  weight  is  such  as  vastly  to  exceed  that 
of  any  one  of  the  planets,  and  indeed  it  rises  so  superior 
to  the  combined  masses  of  all  the  planets  that  the  center 
of  gravity  of  the  system  falls  even  within  the  surface  of 
the  sun.  This  may  be  shown  by  an  examination  of  the 
weights  and  respective  distances  of  the  planets.  We  will 
explain  the  reasoning.  If  the  sun  and  earth  were  equal 
in  weight,  then  the  center  of  gravity  would  lie  in  the 
middle  of  the  line  joining  their  centers ;  but  the  sun  is 
equal  in  weight  to  354,936  earths,  and  hence,  dividing 
the  distance  between  the  centers  (ninety-five  millions  of 
miles)  into  354,936  equal  parts,  the  center  of  gravity 
of  the  sun  and  earth  will  fall  on  the  first  point  of  division 
nearest  the  sun's  center,  that  is  at  a  distance  of  about  267 
miles ;  but  from  the  center  of  the  sun  to  his  surface  is  a 
distance  of  444,000  miles,  and  thus  the  center  of  gravity 
of  the  sun  and  earth  falls  far  within  the  limits  of  the  solar, 
surface. 

The  energy  exerted  by  the  sun  on  any  one  of  his  satel- 
lites is  in  a  constant  state  of  fluctuation,  growing  out  of 
the  variation  in  the  distance  of  the  planet.  The  sun's 
force  decreases  as  the  square  of  the  planet's  distance  in- 
creases. If,  then,  we  take  the  earth's  distance  as  unity, 
and  call  the  force  exerted  on  the  earth  by  the  sun  one, 
the  force  exerted  on  a  planet  twice  as  remote  from  the 
sun  as  the  earth,  would  be  but  one-fourth,  at  .three  times 
the  distance  one-ninth,  at  ten  times  the  distance  it  would 
be  but  one  hundredth  part  of  that  exerted  on  the  earth. 
This  law  of  gravitation  should  be  well  understood3  as  we 


AS    PONDERABLE    BODIES.  319 

shall  have  occasion  to  make  frequent  applications  in  our 
future  examinations. 

POWER   OF   GRAVITATION   ON  THE   SOLAR  SURFACE. — 

If  it  were  possible  to  transport  a  body  weighing  at  the 
earth's  equator  one  pound  to  the  equator  of  the  sun, 
as  the  weight  of  the  body  is  due  to  the  power  of  the 
earth's  attraction,  and  as  the  sun  is  heavier  than  the 
earth  in  the  high  ratio  of  354,936  to  1,  we  might  sup- 
pose that  the  pound  weight  on  the  earth  removed  to  the 
sun  would  be  increased  in  the  same  ratio.  This  would 
be  true  in  case  the  sun's  diameter  were  precisely  equal 
to  that  of  the  earth.  This,  however,  is  not  the  case. 
The  radius  of  the  sun  is  111.454  times  that  of  the  earth, 
and  this  distance  will  reduce  the  attractive  power  of  the 
sun  in  the  ratio  of  (111.645)'  to  (I)2,  or  as  12,442.28  to 
1.  If,  therefore,  we  reduce  354,936  in  the  above  ratio, 
or,  in  other  language,  divide  it  by  12,442.28,  we  obtain 
for  a  quotient  28,  showing  that  a  body  weighing  one 
pound  at  the  earth's  equator  would  weigh  28  pounds  at 
the  sun's  surface.  This  would  be  slightly  reduced  from 
the  uplifting  action  of  the  centrifugal  force  due  to  the 
velocity  of  rotation  of  the  sun  on  its  axis.  This  diminu- 
tion may  be  readily  computed.  We  shall  see  hereafter 
that  the  centrifugal  force  at  the  earth's  equator  is  equal 
to  ^jg-  of  the  force  of  gravity.  Now,  if  the  sun  rotated 
in  the  same  time  as  the  earth,  and  their  diameters  were 
equal,  the  centrifugal  force  on  the  equators  of  the  two 
orbs  would  be  equal.  But  the  sun's  radius  is  about  111 
times  that  of  the  earth,  and  if  the  period  or  rotation  were 
the  same  the  centrifugal  force  at  the  sun's  equator  would 
be  greater  than  that  at  the  earth's,  in  the  ratio  of  (111)1 
to  1,  or  more  exactly  in  the  ratio  of  12,442.28  to  1.  But 
the  sun  rotates  on  its  axis  much  slower  than  the  earth,  re- 


320  THE    SUN    AND     PLANETS 

quiring  more  than  25  days  for  one  revolution.  This  will 
reduce  the  above  in  the  ratio  of  1  to  (25) 2,  or  1  to  625 ; 
so  that  we  shall  have  the  earth's  equatorial  centrifugal 
force  *Jyxl2,442.28-r-625=4«f£tVfJ==0.07  nearly 
for  the  sun's  equatorial  centrifugal  force.  Hence  the 
weight  before  obtained,  28  pounds,  must  be  reduced  seven, 
hundredthsof  its  whole  value,  and  we  thus  obtain  28  — 
0.196—27.804  pounds  as  the  true  weight  of  one  pound 
transported  from  the  earth's  equator  to  that  of  the 
sun. 

These  principles  enable  us  to  compute  readily  the 
gravitating  force  exerted  by  the  sun  at  any  given  dis- 
tance ;  and,  as  we  shall  see  hereafter,  this  mighty  cen- 
tral orb  is  pre-eminently  the  controlling  body  in  the 
scheme  of  revolving  worlds,  which  move  about  him  as 
their  center,  in  obedience  to  the  laws  of  motion  and 
gravitation. 

We  close  what  we  have  to  say  of  the  sun  by  stating 
that  a  heavy  body  weighing,  as  it  does,  28  times  as  much 
at  the  solar  as  at  the  terrestrial  equator,  if  free  to  fall, 
will  pass  over  in  one  second  a  space  equal  to  28  x  16.1= 
450.8  feet. 

PERTURBATIONS  OP  MERCUKY. — In  our  discussion  of 
the  planets  already  given  we  were  only  prepared  to  pre- 
sent the  discoveries  of  formal  astronomy.  These  in- 
volved the  elements  of  the  elliptic  orbits  and  the  ob- 
served circumstances  of  the  planetary  movements.  We 
are  now  prepared  to  understand  how  the  system  of  solar 
satellites  constitutes  a  grand  assemblage  of  worlds  in 
motion  and  yet  in  equilibrio,  so  that,  although  there  be 
fluctuations  to  and  fro,  which  are  really  perpetual,  in  the 
end  the  system  is  stable  and  in  exact  dynamical  counter- 
poise. The  great  law  of  universal  gravitation  being 


AS    PONDERABLE     BODIES.  321 

known,  as  also  the  laws  of  motion,  it  becomes  possible 
to  determine  the  exact  conditions  of  this  mighty  system- 
atic equilibrium,  and  in  a  strict  sense  to  weigh  each  of 
the  worlds  belonging  to  the  system.  Indeed,  this  weight 
or  mass  of  the  planets  must  be  first  ascertained  before  it 
becomes  possible  to  compute  the  influence  exerted  by  one 
body  on  another,  even  when  their  actual  distances  are 
known.  The  distances  being  the  same,  two  bodies  at- 
tract a  third  by  a  force  which  is  in  direct  proportion  to 
their  masses.  Hence,  if  our  moon  could  be  conveyed  suc- 
cessively to  each  of  the  planets  and  be  located  at  the  same 
distance  from  each  it  now  is  from  the  earth,  the  periods 
of  revolution  of  our  satellite  round  any  one  of  these  worlds 
would  show  us  whether  that  world  weighed  more  or  less 
than  ours.  Thus  in  case  the  period  of  revolution  of  the 
moon  around  a  planet  should  be  one-half  its  present 
period,  then  that  planet,  holding,  as  it  does,  the  moon 
with  double  the  velocity  at  the  earth,  it  must  be  double 
the  weight  of  the  earth,  and  so  for  any  other  period. 

It  is  in  this  way  that  we  are  enabled  very  exactly  to 
weigh  the  planets  which  are  surrounded  by  satellites,  as 
we  have  already  seen ;  but  those  planets  which  have  no 
satellite,  such  as  Mercury,  Venus  and  Mars,  can  only  be 
weighed  by  the  effect  they  produce  on  other  bodies  of 
the  system,  and  especially  on  those  vaporous  masses  the 
comets,  which  occasionally  come  sufficiently  near  these 
bodies  to  be  subjected  to  very  powerful  perturbations. 

The  mass  of  Mercury  is,  of  course,  subject  to  some 
uncertainty,  but  as  now  determined,  in  case  the  sun  were 
divided  into  one  thousand  millions  of  equal  parts,  it 
would  require  2,055  of  these  parts  to  be  placed  in  one 
scale  of  a  balance  to  counterpoise  Mercury  in  the  oppo- 
site scale. 

u» 


322  THE    SUN    AND     PLANETS 

Knowing  tbe  mass  of  a  planet  and  its  volume,  we  can 
easily  deduce  its  specific  gravity  or  density.  For  ex- 
ample, the  volume  of  Mercury  is  equal  to  0.595,  the 
earth  being  unity ;  but  the  mass  of  the  earth  in  the  same 
parts  of  the  sun  just  employed,  as  we  shall  see,  is  28,173. 
Hence,  if  these  planets  were  equally  dense,  their  volumes 
would  be  to  each  other  as  28,173  to  2.055,  or  nearly 'as 
13.7  to  1,  or  as  1  to  0.072 ;  but  Mercury's  volume  is  but 
0.595,  the  earth  being  taken  as  unity,  and  hence  Mer- 
cury must  be  denser  than  the  earth  in  the  ratio  of  0.072 
to  0.595,  or  as  1.2  to  1  nearly. 

Thus  are  we  made  acquainted  with  the  very  structure 
or  material  of  the  planets  by  the  process  of  weighing 
them,  revealed  by  the  laws  of  motion  and  gravitation,  and 
that  these  results  cannot  be  much  in  error  is  manifest 
from  the  fact  that  the  transit  of  Mercury  across  the 
sun's  disk,  which  occurred  on  the  8th  May,  1845,  and 
observed  at  the  Cincinnati  Observatory,  the  computed 
and  observed  contact  of  the  planet  with  the  sun's  limb 
differed  by  only  sixteen  seconds  of  time  ! 

This  prediction  also  verifies  the  values  of  the  secular 
inequalities,  or  slow  changes  in  the  element  of  Mercury's 
orbit,  due  to  the  planetary  perturbations,  which  were 
fixed  for  the  beginning  of  the  present  century  as  fol- 
lows : — The  perihelion  makes  an  absolute  advance  each 
year  of  5".8 ;  the  node  recedes  annually  7".8.  The 
eccentricity,  in  terms  of  the  semi-major  axis,  was 
0.210.551.494,  and  its  increase  in  one  hundred  years 
amounts  to  0.000.003.866,  in  terms  of  the  same  unit. 
Let  us  admit  these  changes  to  be  progressive  at  the 
Same  rate,  and  then  convert  them  into  intelligible  terms, 
and  examine  the  results.  The  perihelion  point  advanc- 
ing at  the  rate  of  5". 8  a  year,  will  require  to  pass  ovei 


AS     PONDERABLE     BODIES.  323 


360°,  or  1,296,000  seconds,  ^6tn—  =223,449  years. 
Such  is  the  vast  period  required  for  one  revolution  of 
the  perihelion  point.  In  like  manner  we  may  see  that 
the  node  requires  a  period  exceeding  one  hundred  thou- 
sand years  for  its  revolution. 

The  eccentricity  is  slowly  increasing,  and  if  we  admit 
the  orbit  to  have  been  circular,  and  that  the  present 
figure  has  been  the  result  of  the  annual  change,  acting 
uniformly,  to  produce  the  existing  orbit  must  have  re- 
quired no  less  than  five  million  four  hundred  and  forty- 
six  thousand  years  ! 

The  present  eccentricity  of  the  orbit  of  Mercury  is 
such  that  the  aphelion  distance  exceeds  the  perihelion 
distance  by  more  than  fifteen  millions  of  miles.  The 
energy  exerted  by  the  sun  on  the  planet  at  perihelion, 
as  compared  with  that  exerted  at  aphelion,  may  be  read- 
ily computed  thus  :  Mercury's  greatest  distance  from  the 
sun  amounts  to  about  forty-four  millions  of  miles.  This 
is  about  one  hundred  times  the  solar  radius,  and  at  this 
distance  the  sun's  power  will  be  reduced  to  the  TT£77 
part  of  what  it  is  at  the  sun's  surface,  but  the  planet 
when  nearest  the  sun  is  distant  about  twenty-nine  mil- 
lions of  miles,  that  is,  less  than  seventy  times  the  solar 
radius,  and  hence  the  power  of  gravitation  is  reduced  to 
the  T¥Vo-  Part  °f  what  it  is  at  the  sun's  surface,  or,  what 
comes  to  the  same  thing,  Mercury  at  aphelion  is  attracted 
with  a  force  only  one-half  as  great  as  that  by  which  it  is 
affected  when  nearest  the  sun. 

If  a  person  were  transported  to  the  equator  of  Mer- 

cury, his  weight  would  be  greatly  reduced  from  that  found 

on  the  earth.     The  mass  of  Mercury,  in  terms  of  that  of 

"the  earth  as  unity,  is  but  0.729,  and  if  Mercury's  diam- 

eter were  equal  to  that  of  the  earth,  then  one  pound  on 


324  THE    SUN    AND     PLANETS 

the  earth  would  weigh  0.729  Ibs.  when  removed  to 
Mercury ;  but  as  the  radius  of  Mercury  is  only  1,544 
miles,  or  twenty-six  hundred ths  of  the  earth's  radius, 
this  will  increase  the  weight  in  the  ratio  of  (2.6)2  to  (I)2, 
or  as  6.76  to  1.  Hence,  by  multiplying  0.729  by  6.76, 
we  have  0.493  Ibs.  as  the  weight  of  a  terrestrial  pound 
removed  to  Mercury,  that  is,  the  power  of  gravitation 
on  the  surface  of  this  planet  is  about  one-half  of  what  it  is 
on  the  earth. 

All  the  planets  exterior  to  the  orbit  of  Mercury  exert 
an  amount  of  power  on  this  nearest  planet  to  the  sun 
which  varies  directly  as  the  mass,  and  inversely  as  the 
square  of  the  distance  of  the  disturbing  body.  Let  us 
suppose  the  earth  and  Venus  to  be  in  conjunction  with 
Mercury,  and  that  these  planets  are  at  their  mean  dis- 
tances from  the  sun,  and  let  us  compute  in  this  configu- 
ration the  relative  power  of  the  sun,  of  Venus,  and  of  the 
Earth,  over  Mercury. 


In  the  figure  let  S  represent  the  sun,  M  Mercury,  V 
Venus,  and  E  the  Earth.  Taking  the  distance  S  E  to  be  1. 
S  M  will  be  0.387,  and  S  V  will  be  0.723.  Hence,  M  V 
will  be  equal  to  S  V— S  M=0.723-0.387=0.336,  and 
V  E  will  be  equal  to  S  E— S  V=1.000-0. 723— 0.277. 
As  the  mass  of  Venus  is  but  the  390,000th  part  of  the 
sun's  mass,  her  effect  on  Mercury  at  equal  distances 
would  be  but  one  part  in  three  hundred  and  ninety 
thousand  of  the  sun's  power.  The  fact  that  Venus  is 


AS    PONDERABLE    BODIES.  325 

nearer  Mercury  than  the  sun,  in  the  ratio  of  V  M  to  S  M, 
or  of  0.336  to  0.387,  will  increase  her  relative  power  in 
the  ratio  of  the  squares  of  these  quantities  inversely, 
that  is,  as  (0.336)2  to  (0.387)',  or  as  0.113  to  0.150,  or 
as  1  to  1.3 — that  is,  we  must  multiply  3  gV.o  FO-  by  1.3 
to  obtain  the  effect  of  Venus  on  Mercury,  as  compared 
with  that  of  the  sun ;  in  other  language,  if  the  sun's 
power  over  Mercury  he  divided  into  390,000  equal  parts, 
the  power  of  Venus  over  the  same  planet  will  amount  to 
just  one  and  one-third  of  these  parts. 

Let  us  now  compute  the  attraction  of  the  earth  as 
compared  with  that  of  the  sun.  As  the  earth  weighs  1, 
while  the  sun  weighs  354,936,  at  equal  distances  the 
powers  of  the  earth  and  sun  would  be  as  1  to  354,936 ; 
but  the  distance  S  M  is  0.387,  while  the  distance  M  E 
is  1.000—0.387=0.613.  As  the  sun  is  the  nearer,  his 
power  will  be  increased  in  the  ratio  of  the  square  of  dis- 
tance inversely,  or  as  (0.613)'  to  (0.387)',  or  as  0.376 
to  0.150,  or  as  2.56  to  1 — that  is,  the  earth's  power, 
which  on  account  of  its  mass  is  but  one  part  in  354,936 
of  that  of  the  sun  at  equal  distances,  must  further  be  re- 
duced on  account  of  its  distance  to  a  fraction  of  this  quan- 
tity, represented  by  -^hjj  tha*  is,  in  case  we  divide,the 
sun's  power  of  attraction  upon  Mercury  into  787,340 
parts,  the  attractive  power  of  the  earth  will  be  repre- 
sented by  one  of  these  parts. 

We  have  seen  above  that  the  power  of  Venus  over 
Mercury  is  equal  to  3^;!^,  the  power  of  the  sun  being 
1.  The  power  of  the  earth  is  TJT.T T TJ  or  not  quite  one- 
half  of  the  former  quantity.  Hence  the  disturbing  in- 
fluence of  Venus  is  evidently  the  predominating  one  in 
the  case  of  Mercury. 

It  may  be  well  to  extend  our  investigation  a  little 


326  THE    SUN    AND    PLANETS 

further  and  examine  the  influence  of  the  massive  planet 
Jupiter  on  Mercury,  to  see  whether  Venus  still  pre- 
dominates in  its  power  over  that  of  the  heaviest  planet 
of  the  system.  The  distance  of  Jupiter  from  the  sun  is 
5.2,  that  of  the  earth  being  1.  The  distance  of  the  earth 
from  Mercury  is  0.613.  The  distance  of  Jupiter  from 
Mercury  is  5.200-0.387=4.813.  In  case  the  earth 
and  Jupiter  were  equal  in  mass,  then  the  power  of  Jupi- 
ter over  Mercury  would  be  to  the  power  of  the  earth  as 
(0.613)2  to  (4.813)2,  or  as  0.376  to  23.164,  or  as  1  to 
61.6 — that  is,  Jupiter's  eflect  is  reduced  to  the  fraction 
¥  i  _  of  what  it  would  be  at  a  distance  from  Mercury  equal 
to  thaf  of  the  earth ;  but  this  is  supposing  the  earth  and 
Jupiter  to  be  equal  in  mass,  whereas  Jupiter  really  re- 
quires 338  earths  to  counterpoise  his  weight.  We  must, 
therefore,  increase  the  fraction  ^j-^-g-  338  times,  and  we 
have  -|f. \— 5.5  about.  Hence,  Jupiter  exerts  a  power 
over  Mercury  when  in  conjunction  5.5  times  as  great  as 
that  exerted  by  the  earth,  or  two  and  a  half  times  greater 
than  the  attraction  of  Venus. 

These  computations  have  been  made  to  show  how  min- 
ute a  portion  of  the  sun's  power  is  that  exerted  by  any 
planet  to  disturb  the  motions  of  another  planet,  and  also 
to  show  that  we  cannot  neglect  any  disturbing  body  be- 
cause of  the  grea.t  distance  at  which  it  may  be  placed. 

It  will  be  readily  seen  that  when  Mercury  is  in  oppo- 
sition with  respect  to  Venus,  her  power  is  greatly  re- 
duced on  account  of  the  increased  distance  by  which  the 
planets  will  be  then  separated.  Indeed,  the  attractive 
force  computed  at  conjunction  will  be  reduced  to  about 
one-tenth  at  opposition. 

This  is  not  true,  however,  of  the  attractive  power  of 
Jupiter.  The  distance  4.813  in  conjunction  will  only  bo 


AS    PONDERABLE     BODIES.  327 

increased  by  the  diameter  of  Mercury's  orbit,  or  by 
2(0.387) =0.774  when  in  opposition,  and  the  distances 
will  stand  4.813  and  6.587.  Jupiter's  power  at  the  in- 
creased distance  will  be  reduced  only  in  the  ratio  of  tho 
square  of  4.813  to  that  of  6.587,  or  about  as  1  to  2. 
.  As  an  exercise  the  student  should  compute  the  energy 
exerted  by  the  other  planets  over  Mercury,  and  thus  ob- 
tain a  familiarity  with  the  application  of  the  law  of  gravi- 
tation to  the  problems  of  nature. 

"While  we  are  writing  the  intelligence  has  reached  this 
country  that  a  new  planet  has  actually  been  discovered, 
revolving  in  an  orbit  between  Mercury  and  the  sun. 
M.  Le  Verrier  some  time  since  announced  that  there 
were  perturbations  in  the  elements  of  the  orbit  of  Mer- 
cury not  explained  by  any  of  the  known  causes,  and 
hence  he  drew  the  conclusion  that  possibly  a  ring  of  very 
small  planets  were  revolving  within  the  limits  of  Mer- 
cury's orbit.  One  of  these  minute  planets  is  said  to  have 
been  actually  seen  more  than  once  by  an  amateur  as- 
tronomer, whose  name  is  M.  Lescarbault.  This  planet  is 
said  to  complete  its  revolution  in  about  three  weeks,  and 
hence  its  distance  from  the  sun  must  be  about  fourteen 
or  fifteen  millions  of  miles. 

VENUS   CONSIDERED   AS  A   PONDERABLE    BODY. — The 

angle  subtended  by  this  planet  at  its  mean  distance  from 
the  earth  amounts  to  17'/.55,  showing  an  actual  diameter 
nearly  equal  to  that  of  the  earth.  The  weight  or  mass 
of  Venus  is  not  so  well  determined  as  that  of  the  planets 
attended  by  satellites,  yet  we  have  reason  to  believe  that 
the  approximate  value  does  not  differ  by  any  very  con- 
siderable amount  from  the  true  one.  As  now  deter- 
mined by  the  best  authorities,  Venus  weighs  0.900,  the 
•weight  of  the  earth  being  assumed  as  1.000.  If  an  in- 


328  THE    SUN    AND     PLANETS 

habitant  of  the  earth  were  transported  to  Venus,  his 
weight  would  be  reduced  in  the  ratio  of  1  to  0.94,  and  a 
heavy  body,  free  to  fall,  would  pass  over  15.1  feet  in  the 
first  second  of  time.  Here  we  might  repeat  the  reason- 
ing already  employed  in  the  case  of  the  sun  to  reach 
these  results,  but  as  we  shall  have  occasion  hereafter 
to  apply  the  reasoning  to  the  cases  of  the  larger  plan- 
ets, we  shall  merely  refer  to  the  demonstration  already 
made. 

All  the  elements  of  the  orbit  of  Venus  are  in  a  state  of 
constant  fluctuation.  The  exact  condition  of  these  elements 
will  be  given  hereafter,  as  well  as  the  measured  amount  of 
the  changes.  We  find  in  Venus  the  first  example  of  a  re- 
markable perturbation  arising  from  a  cause  already  ad- 
verted to,  viz. :  an  approximate  coinmensurability  between 
the  periods  of  revolution  of  Venus  and  the  earth.  The 
planet  performs  her  revolution  around  the  sun  in  224.700 
days,  while  the  earth  occupies  365.25  days  in  accom- 
plishing her  revolution.  If  we  multiply  224.7  by  13  we 
obtain  2,921.10;  multiply  365.256  by  8,  and  we  have 
2,922.048.  Thus  we  perceive  that  in  case  Venus  and 
the  earth  are  in  conjunction  on  any  given  day,  at  the  end 
of  2,921  days  they  will  be  nearly  in  conjunction  again  at 
the  same  points  of  their  orbits.  Whatever  perturbation 
the  one  planet  produces  on  the  other  will  be  again  re- 
peated on  the  return  of  the  same  identical  configuration. 
But  we  have  already  seen  that  the  synodical  revolution 
of  Venus  is  accomplished  in  583.9  days.  This  quantity, 
multiplied  by  5,  produces  2,919.6 — that  is,  during  the 
time  involved  in  the  long  cycle  of  2,921  days  there  have 
occurred  five  conjunctions  of  the  earth  and  Venus  dis- 
tributed equally  around  the  orbits  of  the  planets.  If  we 
examine  the  figure  below,  and  suppose  S,  V  and  E  to 


AS    PONDERABLE    BODIES.  329 

represent  the  places  of  the  sun,  of  Venus  and  the  earth, 
at  the  commencement  of  a  great  cycle  of  2,921  days,  at 
the  end  of  one  synodic  revolution  of  Venus  V'  and  E 
will  be  the  places  of  the  two  planets.  At  the  end  of  the 

E 


second  synodic  revolution  the  planets  will  be  in  V"  and 
and  E",  and  thus  they  will  pass  round  the  orbits,  mak- 
ing their  conjunctions  at  intervals  of  583.9  days,  and 
separated  by  arcs  equal  to  one-fifth  part  of  360°.  Let 
us  now  carefully  examine  the  reciprocal  influence  of  V 
and  E.  Starting  from  the  places  V  and  E  in  the  figure, 
Venus  will  take  the  lead,  and  will  tend  to  drag  forward 
the  earth,  while  the  earth  will  pull  back  the  planet,  and 
as  the  planets  sweep  around  the  sun,  Venus  overtakes  the 
earth  at  V'"'  E"",  and  as  the  earth  is  now  in  advance, 
it  will  accelerate  Venus,  and  will  in  turn  be  retarded. 
Thus  a  partial  compensation  is  effected,  and  the  motions 
of  the  planets  return  nearly  to  what  they  were  at  the 


330  THE    SUN    AND     PLANETS 

start.  This  same  process  is  repeated  at  every  conjunc- 
tion ;  and  in  case  the  planets  fall  exactly  on  the  right 
line  S  V  E.  at  the  end  of  five  of  these  conjunctions  a 
complete  restoration  would  be  effected.  But  this  is  not 
exactly  true.  The  periods  are  not  precisely  equal,  and 
the  fifth  conjunction  does  not  fall  on  S  Y  E,  but  on  a 
dotted  line  a  little  behind  the  position  S  V  E.  There 
will,  therefore,  remain  a  very  small  amount  of  outstand- 
ing perturbation  at  the  close  of  one  great  cycle,  which 
will  go  on  accumulating  so  long  as  the  dotted  line  falls  in 
the  same  half  of  the  earth's  orbit.  But  the  difference 
between  2,921.160  days  and  2,922.048  is  0.852,  and  by 
this  fraction  of  one  day  is  the  earth  later  than  Venus  in 
reaching  the  point  of  departure.  Hence,  the  conjunction 
of  the  planets  must  have  taken  place  on  a  line  behind 
that  of  the  former  conjunction,  whose  position  may  be 
readily  computed.  The  daily  motion  of  Venus  is  1°.612, 
while  that  of  the  earth  is  0°.985,  and  thus  Venus  gains 
daily  on  the  earth  by  an  amount  equal  to  1°.612— 
0°.985=0°.627.  Let  S  V  E  be  the  line  of  the  first 


conjunction.  At  the  end  of  thirteen  revolutions  of  Venus 
she  returns  to  the  point  V,  while  the  earth  is  in  the 
point  E',  requiring  yet  0.852  days  to  reach  E.  Venus 
must,  therefore,  have  passed  the  earth  on  some  line  as 
S  V"  E",  such  that  Venus  will  have  gained  0.852  days 
on  the  earth  when  she  arrives  at  V.  But  the  daily  mo- 
tion of  Venus  is  1°.612,  and  in  the  fraction  of  one  day 
0.852,  she  will  move  I°.612x0.852^1°.373.  Hence, 


AS    PONDERABLE    BODIES.  381 

the  new  line  of  conjunction  S  V"  E''  must  fall  behind 
the  old  line  by  this  amount  in  each  great  cycle  of  thir- 
teen revolutions  of  Venus  and  eight  revolutions  of  the 
earth. 

At  the  end  of  a  great  cycle,  formed  by  dividing  360° 
by  1°.373,  and  multiplying  the  quotient  by  8,  the  line 
of  conjunction  will  return  to  its  former  position ;  and  in 
case  the  orbits  remain  circular,  all  the  perturbations  of 
both  the  planets  resulting  from  this  cause,  as  affecting 
the  orbital  velocities  and  consequently  the  lengths  of  the 
major  axes,  will  have  been  completely  obliterated.  The 
orbits  are,  however,  not  exact  circles,  neither  are  the 
elements  invariable,  and  hence  the  restoration  will  not 
be  perfect  even  at  the  end  of  this  great  cycle;  but  as  the 
changes  are  all  periodical,  and  as  the  lines  of  apsides  re- 
volve entirely  around,  periodicity  again  marks  these 
minute  perturbations,  and  at  the  end  of  a  grand  cycle, 
composed  of  many  subordinate  ones,  these  complexities 
and  modifications  will  all  be  entirely  swept  away,  and 
the  system  return 'to  its  primitive  condition.  The  singu- 
lar equation  (as  it  is  called)  above  described  in  the  mean 
motions  of  Venus  and  the  earth  was  first  detected  by 
the  present  Astronomer  Royal.  The  period  is  about  240 
years,  and  in  the  whole  of  this  time  the  accumulated 
effect  on  the  longitude  of  Venus  cannot  exceed  2".95, 
while  its  effect  on  that  of  the  earth  only  reaches  2'/.06. 
This  result  of  computation  yet  remains  to  be  verified  by 
actual  observation. 

For  other  particulars  of  the  characteristics  of  this 
planet  and  of  the  elements  of  its  orMt  we  refer  the 
reader  to  the  Appendix. 

THE  EARTH  AND  MOON  AS  PONDERABLE  BODIES. — We 

have  already  determined  the  weight  of  the  earth  in  terms 


332  THE    SUN    AND    PLANETS 

of  that  of  the  sun,  and  we  have  seen  that  it  would  require 
354,936  earths  like  ours  to  balance  the  ponderous  orb 
which  occupies  the  focal  point  of  the  solar  system.  It 
remains  now  to  determine  the  absolute  weight  of  the 
earth  in  pounds  avoirdupois.  We  shall  assume  water  as 
the  standard,  and  admit  that  one  cubic  foot  of  water 
weighs  62.3211  Ibs.  From  the  known  magnitude  of  the 
sphere  of  the  earth,  assuming,  say,  the  mean  diameter  to 
be  7,912.41  miles,  we  can  obtain  the  solid  contents  in 
cubic  miles,  amounting  to  no  less  than  259,373  millions. 
The  number  of  cubic  feet  in  a  cubic  mile  is  readily  com- 
puted, being  equal  to  5,280x5,280x5,280.  Thus  if 
we  knew  the  weight  of  one  cubic  foot  of  the  earth,  in 
terms  of  the  weight  of  one  cubic  foot  of  water,  the  total 
weight  of  the  entire  globe  could  be  readily  obtained  in 
pounds. 

This  weighing  of  the  earth,  absolutely,  is  a  problem  of 
great  difficulty,  yet  it  has  been  executed,  and  the  final 
results,  though  not  precisely  accurate,  are,  no  doubt, 
close  approximations.  We  can  only  give  a  general  out- 
line of  the  principle  involved  in  the  method  employed. 
Suppose  an  inflexible  rod  with  a  small  leaden  ball  at 
each  extremity  suspended  in  the  middle  by  a  delicate 
wire.  When  absolutely  at  rest  the  wire  will  hang  ver- 
tically without  twisting  or  torsion.  Any  force  applied 
to  either  leaden  ball  to  move  it  horizontally  will  tend  to 
twist  the  suspending  wire,  and  this  torsion  will  resist  the 
action  of  the  force,  and  this  resistance  will  finally  be 
brought  into  equilibrium  with  the  force,  and  will  thus  in 
some  sense  beco^  its  measure.  Thus  in  case  a  delicate 
weight  is  attached  to  one  of  the  leaden  balls  and  suspended 
over  a  pulley,  it  will  descend  until  the  torsion  of  the 
wire  shall  be  such  as  to  exactly  balance  the  small  weight, 


AS    PONDERABLE    BODIES. 


and  then  the  torsion  and  weight  will  stand  in  equilibrio, 
and  the  value  of  the  weight  (friction  out  of  considera- 
tion) measures  the  force  of  resistance  to  torsion.  Sup- 
pose a  divided  scale  placed  beneath  the  leaden  ball,  and 
a  needle  used  as  a  pointer,  then  as  the  ball  moves  over 
this  scale,  a  microscope  properly  adjusted  may  read  the 
amount  of  motion  with  the  greatest  delicacy. 

This  machinery  being  arranged,  suppose  we  bring  a 
leaden  ball  one  foot  in  diameter  to  within,  say  six  inches 
of  the  small  ball.  Its  power  of  attraction  will  move  this 
ball  over  a  space  easily  read  off  from  the  divided  scale, 
and  this  will  measure  the  attractive  force  of  the  large 
leaden  ball. 

Having  thus  learned  the  power  exerted  by  a  leaden 
ball  one  foot  in  diameter,  on  a  material  point  located  one 
foot  from  its  center,  it  is  easy,  from  the  principles  already 
laid  down,  to  compute  what  would  be  the  attractive 
power  of  a  globe  of  lead  as  large  as  the  earth  ;  and  in 
case  this  power  of  attraction  thus  computed  should  be 
precisely  equal  to  that  exerted  by  the  earth,  then  the 
earth  must  weigh  exactly  as  much  as  the  leaden  globe  of 
equal  size.  This,  however,  is  found  from  many  experi- 
ments, tried  with  the  most  refined  apparatus,  not  to  be 
the  case.  The  leaden  globe  is  much  heavier  than  the 
earthen  one,  and,  indeed,  we  find  that  one  cubic  foot  of 
earth  of  the  mean  density  of  the  whole  globe  is  as  heavy 
as  about  five  and  a  half  cubic  feet  of  water.  Hence, 
every  cubic  foot  of  the  earth  weighs  on  the  average 
62.3211  x  5.5=342.76  Ibs. ;  and  as  there  are  in  the  en- 
tire globe  259,373  millions  of  cubic  miles,  the  whole 
globe  must  weigh  as  many  million  pounds  as  are  expiessed 
by  the  product  259,373  x  (5280) 3  x  342.76. 

With  this  knowledge  of  the  absolute  weight  of  our 


334  THE    SUN    AND     PLANETS 

earth  it  is  easy  to  obtain  the  weight  of  the  sun  and  plan- 
ets in  pounds,  were  it  necessary.  Multiply  the  number 
of  pounds  in  the  weight  of  the  earth  by  354,936,  and  we 
obtain  the  actual  weight  of  the  sun. 

THE  FIGURE  OF  THE  EARTH.—  We  have  already  seen 
that  the  earth  is  not  a  sphere,  but  a  spheroid,  protuber- 
ant at  the  equator  and  flattened  at  the  poles.  The  exact 
methods  of  astronomy  employed  in  the  measurement  of 
arcs  of  the  earth's  meridians,  together  with  the  vibra- 
tions of  the  pendulum  in  different  latitudes,  have  fixed 
with  great  accuracy  the  relative  values  of  the  polar  and 
equatorial  diameters  of  the  earth.  The  mean  of  a  large 
number  of  measures  results  in  giving  the — 

Equatorial  diameter, 41. 847, 192  feet. 

Polar  diameter, 41,707,324    " 

This  gives  a  compression  of       .        .        .        .          139,768    ' 

Some  very  remarkable  results  flow  from  this  peculiar 
figure  of  the  earth.  Among  these  we  shall  consider  first 
the  equilibrium  of  the  ocean.  If  it  be  true,  as  just 
asserted,  that  the  equatorial  diameter  of  our  globe  ex- 
ceeds the  polar  diameter  by  139,768  feet,  then  in  case 
the  earth  were  reduced  to  the  figure  of  an  exact  sphere, 
by  turning  off  the  redundant  matter,  we  should  be  com- 
pelled to  turn  down  at  the  equator,  to  a  depth  of  no  less 
than  69,884  feet  (one-half  of  the  above  quantity),  and 
hence  the  equatorial  region  may  be  considered  as  a  vast 
mountain  range,  belting  the  whole  earth,  and  rising 
above  the  general  level  nearly  seventy  thousand  feet. 
On  the  sides  and  over  the  summit  of  this  mountain  range 
the  ocean  sleeps  its  currents  and  its  tides,  and  yet  the 
most  delicate  and  beautiful  equilibrium  is  maintained. 

This  is  due  to  the  fact  that  the  velocity  of  rotation  of 


AS    PONDERABLE     BODIES.  335 

the  earth  on  its  axis  is  absolutely  uniform  and  invariable, 
and  hence  the  centrifugal  force,  whose  power  precisely 
counterbalances  the  gravity  on  the  mountain  side  on  which 
the  ocean  rests,  is  ever  the  same.  This  great  principle  is 
beautifully  exemplified  by  taking  a  glass  vase,  filling  it 
with  a  colored  liquid,  and  suspending  it  by  a  cord.  So 
long  as  the  vase  is  at  rest  the  fluid  on  its  upper  surface  is 
precisely  level  and  plain.  Now,  give  to  the  vase  a  mo- 
tion of  rotation  about  a  vertical  axis  (as  by  the  untwist- 
ing of  the  suspending  cord),  and  at  once  the  fluid  com- 
mences to  rise  upon  the  sides  of  the  vase,  and  a  disk-shaped 
cavity  is  formed.  This  rising  continues  so  long  as  the 
velocity  of  rotation  increases.  Should  the  velocity  be- 
come uniform,  then  the  figure  of  the  fluid  in  the  vase 
assumes  a  form  of  exact  equilibrium,  and  the  delicate 
circle  that  marks  the  height  to  which  the  fluid  rises  in 
the  vase  remains  constant,  and  will  so  continue,  so  long 
as  the  Velocity  of  rotation  is  unchanged.  The  stability 
of  the  figure  of  the  ocean  depends  on  the  same  principle, 
and  were  it  possible  to  arrest  the  rotation  of  the  earth, 
instantly  the  equatorial  ocean  would  rush  towards  the 
poles  and  would  there  rise  until  the  general  level  should 
become  such  as  is  due  to  a  spherical  figure,  which  the 
ocean  would  assume. 

NUTATION  AND  PRECESSION. — We  have  in  these  re- 
markable phenomena  another  effect  of  the  figure  of  the 
earth.  We  have  already  mentioned  the  fact  that  the 
vernal  equinox  (the  point  in  which  the  sun's  center 
crosses  the  equinoctial  in  the  spring  season),  does  not  re- 
main fixed  in  the  heavens.  This  discovery  was  made  by 
the  early  astronomers,  the  fact  noted,  and  an  approximate 
period  of  revolution,  amounting  to  some  twenty-five  or 
twenty-six  thousand  years.  Modern  science  has  not  only 


THE    SUN    AND     PLANETS 

determined  the  exact  period  to  be  25,868  years,  but  has 
traced  the  phenomenon  to  its  origin,  and  has  revealed  the 
cause  to  lie  in  the  fact  that  the  protuberant  mass  of  mat- 
ter surrounding  the  equator  of  the  earth  is  a  sufficient 
purchase  to  enable  the  sun  and  moon  to  tilt  the  entire 
earth,  and  consequently  the  plane  of  the  earth's  equa- 
tor. Suppose  the  earth  revolved  on  an  axis  perpen- 
dicular of  the  ecliptic,  or  that  the  equator  of  the  earth 
and  the  ecliptic  coincided.  Then,  so  far  as  the  sun  is 
concerned,  there  could  arise  no  power  to  effect  a  change 
in  the  plane  of  the  equator ;  but  as  the  moon  revolves  in 
an  orbit  inclined  to  the  plane  of  the  ecliptic,  the  moon 
will  be  sometimes  above  and  sometimes  below  the  plane 
of  the  earth's  equator,  now  supposed  to  be  coincident 
with  the  ecliptic.  Whenever  the  moon  is  above  the  equa- 
torial ring  of  the  earth,  she  will  tend  to  lift  the  nearest 
portion  vof  that  ring  above  the  ecliptic,  and  to  sink  the 
opposite  part  below  the  same  plane,  and  as  the  moon  re- 
volves around  the  earth,  she  will  cause  the  equatorial 
ring  to  tilt  towards  her  position,  and  thus  the  line  of 
nodes  of  the  ring  will  revolve  as  do  the  lines  of  nodes  of 
the  planetary  orbits ;  and  this  is  precisely  what  we  find 
to  be  true  of  the  line  of  equinoxes,  or  the  line  cut  by  the 
plane  of  this  equatorial  ring  from  the  plane  of  the  eclip- 
tic, producing,  as  we  have  seen,  a  retrocession  of  the 
equinoctial  point,  and  a  precession  of  the  time  of  the 
equinox. 

THE  NUTATION  or  THE  EARTH'S  AXIS  is  a  phenomenon 
springing  out  of  the  same  causes  producing  precession. 
If  we  consider  the  axis  of  the  earth  as  an  inflexible  bar, 
passing  through  the  earth's  center  and  perpendicular  to 
the  equator,  extending  indefinitely  in  opposite  directions, 
to  the  celestial  sphere,  it  is  clear  that  any  tilting  of  the 


AS    PONDERABLE    BODIES.  337 

earth's  equatorial  ring  will  equally  tilt  the  axis  of  the 
earth.  This  is  actually  seen  in  the  slow  revolution  of 
the  pole  of  the  earth's  equator  around  the  pole  of  the 
ecliptic  in  a  period  precisely  equal  to  that  employed  in 
the  revolution  of  the  equinoxes.  Nutation  is  but  a  su- 
bordinate fluctuation  whereby  the  pole  of  the  equator, 
instead  of  describing  an  exact  circle  around  the  pole  of 
the  ecliptic,  makes  certain  short  excursions  a  little  on  the 
inside  and  on  the  outside  of  this  circle,  in  a  period  which 
agrees  exactly  with  that  occupied  by  the  revolution  of  the 
nodes  of  the  moon's  orbit.  This  at  once  suggests  the 
moon  to  be  the  principal  cause  of  this  nodding  of  the 
earth's  axis,  and,  indeed,  modern  analysis  has  pointed  out 
the  origin  of  the  movement,  and  has  accurately  computed 
its  value. 

In  all  we  have  said  we  have  supposed  the  equator  and 
ecliptic  to  coincide.  This,  however,  is  not  the  case  of 
nature.  These  planes  are  inclined  to  each  other,  and 
hence  we  find  the  sun  producing  results  (analogous  to 
those  already  traced  to  the  moon)  on  the  mass  of  pro- 
tuberant matter  surrounding  the  earth's  equator.  The 
exact  values  of  these  constants  of  precession  and  nuta- 
tion will  be  found  in  the  Appendix.  The  greatest  pains 
have  been  bestowed  on  their  determination,  as  they  are 
of  the  first  importance  in  fixing  the  absolute  places  of  all 
the  heavenly  bodies. 

FIGURE  OF  THE  EARTH'S  ORBIT. — The  ellipticity  of 
the  earth's  orbit  is  slowly  wearing  away,  under  the  com 
bined  influence  of  all  the  planets.  The  eccentricity  at 
the  commencement  of  the  present  century  amounted  to 
0.016783568,  the  semi-major  axis  being  considered  as 
unity.  The  amount  by  which  this  quantity  is  decreased 
in  a  hundred  years  is  0.00004163.  Let  us  reduce  these 

15 


THE    SUN    AND     PLANETS 

figures  to  intelligible  quantities.  The  eccentricity  is  the 
distance  from  the  center  of  the  ellipse  to  the  focus,  and  in 
miles  is  equal  to  0.016783568  x  95,000,000=1,594,100. 
This  quantity  decreases  in  one  hundred  years  by 
0.00004163x95,000,000=3,954.85  miles.  If,  now, 
we  divide  1,594,100  by  3,954.85,  the  quotient  405+  will 
be  the  number  of  centuries  which  must  elapse  before  the 
earth's  orbit  will  become  an  exact  circle  at  the  present 
rate  of  change.  It  is  ascertained  by  a  rigorous  analytical 
investigation  of  this  great  problem  that  so  soon  as  the 
circular  figure  is  reached  by  the  earth's  orbit  the  same 
causes  reverse  their  effects,  and  the  circular  figure  is  lost, 
and  the  eccentricity  of  the  elliptic  figure  slowly  increases 
until  finally,  at  the  end  of  a  vast  period,  the  original  form 
of  the  orbit  is  regained,  to  be  again  lost,  and  thus  an  ex- 
pansion and  contraction  marks  the  history  of  the  earth's 
orbit,  vibrating  through  periods  of  time  swelling  into  mil- 
lions of  years. 

ACCELERATION  OF  THE  MOON'S  MEAN  MOTION. — This 
change  in  the  figure  of  the  earth's  orbit  produces  a 
minute  change  in  the  mean  motion  of  the  moon,  which 
was,  after  long  years  of  the  most  laborious  research, 
finally  traced  to  its  true  origin  by  La  Place.  The  fact 
that  the  moon  was  moving  faster  in  modern  than  in 
ancient  times  became  evident  from  a  comparison  of  the 
modern  and  ancient  eclipses.  These  eclipses  can  only 
occur  when  the  sun,  earth  and  moon  occupy  the  same 
right  line  nearly,  and  hence  their  record  gives  a  very 
precise  knowledge  of  the  relative  position  of  these  three 
bodies.  It  thus  became  manifest  that  the  average  speed 
with  which  the  moon  was  moving  in  her  orbit  was  slowly 
increasing  from  century  to  century.  This  follows  neces- 
sarily from  the  fact  that  the  loss  of  eccentricity  by  the 


AS    PONDERABLE    BODIES.  339 

orbit  removes  the  earth  by  a  small  amount  (on  the  aver- 
age) further  from  the  sun.  This  carries  both  the  earth 
and  her  satellite  by  so  much  away  from  the  disturbing 
influence  of  the  sun,  leaving  to  the  earth  a  more  exclusive 
control  of  the  moon.  As  the  sun  is  outside  the  moon's 
orbit  with  reference  to  the  earth,  his  attraction  will  in- 
crease the  magnitude  of  the  moon's  orbit,  and,  of  course, 
her  periodic  time.  Any  diminution  of  the  sun's  disturb- 
ing power  will  therefore  by  so  much  permit  the  moon  to 
approach  the  earth,  and  to  increase  her  velocity  of  revo- 
lution ;  and  this  is  precisely  what  observation  has  re- 
vealed with  reference  to  our  satellite  during  the  entire 
period  that  history  has  recorded  the  progress  of  as- 
tronomy. 

This  gradual  acceleration  must  continue  up  to  the  time 
when  the  earth's  orbit  shall  become  exactly  circular  in 
form.  This  limit  once  attained,  as  this  orbit  slowly  re- 
sumes its  elliptic  form,  the  acceleration  of  the  moon's 
mean  motion  is  converted  into  retardation,  and  thus  at 
the  end  of  a  mighty  period  this  change  will  be  entirely 
destroyed,  and  the  moon  and  earth  return  to  their  primi- 
tive condition.  This  acceleration  of  the  mean  motion  of 
the  moon  is  so  slow  that  from  the  earliest  record  of 
eclipses  by  the  Babylonians  down  to  the  present  time, 
some  2,500  years,  the  moon  has  got  in  advance  of  her 
mean  place  by  about  three  times  her  own  diameter. 

The  facts  above  related  indicate  with  how  much  dili- 
gence the  moon's  motions  have  been  studied.  Though 
she  is  our  nearest  neighbor,  and  consequently  more  di- 
rectly under  the  eye  of  the  astronomer  than  any  other 
heavenly  body,  her  motions  have  been  more  complex  and 
difficult  of  perfect  exposition  than  any  object  in  the 
heavens.  The  recent  investigations  of  the  European  and 


340  THE    SUN    AND     PLANETS 

American  astronomers  and  mathematicians  seem  to  have 
finally  conquered  this  refractory  satellite,  so  that  now  it 
becomes  possible  to  unravel  her  involved  and  intricate 
march  among  the  stars  with  such  precision  that  we 
can  fix  her  place  with  certainty  for  even  thousands  of 
years. 

MARS  AS  A  PONDERABLE  BODY. — This  planet  revolves 
in  an  orbit  of  such  eccentricity  as  to  present  very  marked 
differences  in  the  power  of  attraction  of  the  sun  on  the 
planet  when  at  its  greatest  and  least  distances.  Its  mean 
distance  is  142  millions  of  miles,  giving  its  semi-major 
axis  a  length  equal  to  71  millions  of  miles.  The  eccen- 
tricity of  the  orbit  (the  distance  between  the  center  and 
focus  of  the  ellipse)  amounts  to  nearly  one-tenth  of  this 
quantity,  or  to  about  6.4  millions  of  miles.  Hence,  the 
perihelion  distance  is  64.6  millions  of  miles,  while  the 
aphelion  distance  is  77.4  millions  of  miles.  The  attrac- 
tive power  exerted  by  the  sun  in  perihelion  will  be 
greater  than  that  exerted  in  aphelion  in  the  ratio  of 
(77.4)'  to  (64.6)",  or  as  5,991  to  3,172,  or  nearly  as  3 
to  2.  To  resist  this  increased  power  of  attraction  in 
perihelio  the  planet  must  there  move  with  a  far  higher 
velocity  than  when  in  its  aphelion.  All  these  deductions 
from  theory  are  verified  by  observation. 

It  was  from  an  examination  of  the  movements  of  Mars 
that  Kepler  deduced  his  celebrated  laws.  These  laws  we 
have  had  occasion  to  use  constantly  in  our  computations, 
but  in  consequence  of  the  mutual  actions  of  the  planets, 
not  one  of  these  laws  is  rigorously  true.  The  orbits  of 
the  planets  are  not  exact  ellipses,  nor  do  they  so  revolve 
that  the  lines  joining  them  with  the  sun  sweep  over  pre- 
cise equal  spaces  in  equal  times,  nor  are  the  squares  of 
the  periods  of  revolution  precisely  proportional  to  the 


AS    PONDERABLE    BODIES.  341 

cubes  of  the  mean  distances ;  but  the  failure  in  these 
laws  is  due  entirely  to  mere  perturbation,  and  in  case  a 
single  planet  existed  revolving  around  the  sun,  they 
would  all  be  scrupulously  fulfilled. 

The  planet  Mars  was,  however,  well  situated  for  the 
examination  conducted  by  Kepler.  This  becomes  mani- 
fest if  we  call  to  mind  the  great  distance  separating  Mars 
and  Jupiter,  and  the  comparatively  small  disturbance 
which  the  earth  can  produce.  To  present  this  problem 
still  clearer  let  us  suppose  the  earth,  Mars  and  Jupiter  to 
be  in  conjunction,  and  situated  as  in  the  figure.  Then 


1 

]               1 

s            fl 

:            |M 

the  distance  from  S  to  E  is  95  millions  of  miles,  from  S 
to  M  142  millions,  from  S  to  J  890  millions  of  miles. 
Hence,  the  distance  E  M  is  142—95=47  millions  of 
miles,  while  the  distance  M  J  is  890—142=648  millions 
of  miles.  We  will  first  compute  the  power  of  attraction 
of  Jupiter  on  Mars,  as  compared  with  the  power  of  the 
sun.  If  the  masses  were  equal  the  energy  of  Jupiter 
would,  on  account  of  the  greater  distance,  be  reduced  be- 
low that  of  the  sun  in  the  ratio  of  (142)2  to  (648)7,  or 
nearly  as  1  to  21.  But  the  masses  are  not  equal,  for  the 
sun  weighs  as  much  as  3,502  such  globes,  as  Jupiter, 
and  hence,  by  combining  these  causes  of  reduction,  we 
find  the  force  exerted  by  Jupiter  to  be  less  than  that 
exerted  by  the  sun  in  the  ratio  of  1  to  3,502  x  21,  or  as 
1  to  73,542. 

Let  us  now  see  what  force  the  earth  exerts  on  Mars, 
when  compared  with  the  sun's  force.    As  the  earth  is 


842  THE    SUN    AND    PLANETS 

nearer  to  Mars  than  the  sun,  in  case  the  sun  and  earth 
were  of  equal  weights  their  energy  at  Mars  would  be  in 
the  ratio  of  (142)a  to  (47)2,  or  as  20,164  to  2,209,  or 
nearly  in  the  ratio  of  9  to  1.  But  the  sun  weighs  as 
much  as  354,936  earths,  and  if  we  divide  354,936  by  9, 
we  obtain  39,437  as  a  quotient,  and  hence  the  power  of 
the  sun  on  Mars  is  to  the  power  of  the  earth  as  39,437 
tol. 

It  is  thus  seen  that  the  earth  is  more  powerful  than 
Jupiter  to  disturb  Mars  in  the  ratio  of  73,542  to  39,437, 
or  in  the  ratio  of  about  2  to  1.  To  exhibit  more  clearly 
the  minute  character  of  the  effects  of  the  earth  and  of 
Jupiter  on  this  planet,  let  us  compute  the  space  through 
which  a  body  would  fall  in  one  second,  if  as  far  removed 
from  the  sun  as  Mars.  We  have  already  seen  that 
gravity  at  the  solar  surface  is  28.7  greater  than  at  the 
surface  of  the  earth.  At  the  earth  gravity  impresses 
such  a  velocity  on  a  falling  body  that  it  passes  over  a 
space  of  16.1  feet  in  the  first  second  of  time  ;  therefore, 
a  body  at  the  sun's  surface  would  fall  through  a  space 
represented  by  28.7x16.1—461  feet  in  the  first  second 
of  its  fall.  If  we  remove  the  falling  body  to  double  the 
distance  from  the  sun's  center,  the  force  of  the  sun's 
gravity  is  reduced  to  one  quarter,  and  hence  the  space 
passed  over  by  the  falling  body  at  two  units  from  the 
center  of  the  sun  will  be  4-f  ^=115.25  feet.  But  Mars' 
distance  from  the  sun  is  142  millions  of  miles,  while  the 
solar  radius  is  441,500  miles  ;  in  other  words,  a  falling 
body,  removed  to  the  distance  of  Mars  from  the  sun,  is 
about  320  times  more  remote  from  the  sun's  center  than 
when  on  the  sun's  surface,  and  the  energy  of  the  sun's 
gravity  would  be  reduced  at  this  distance  in  the  ratio  of 
(l)a  to  (320)*,  or  asl  to  1,02400;  so  thatabody  would  fall 


AS    PONDERATE     BODIES.  343 

in  one  second,  if  as  far  removed  from  the  center  of  the 
sun  as  is  the  planet  Mars,  through  a  space  represented 
by  ToWo o  =  .0045019  feet.  To  what  extent  will  this 
quantity  be  affected  by  the  attraction  of  the  earth  ?  The 
answer  is  given  in  the  result  already  reached  that  the 
power  of  the  earth  is  only  the  thirty-nine  thousand  four 
hundred  and  thirty-seventh  part  of  that  of  the  sun,  and 
hence  the  falling  body  will  only  pass  over  the  additional 
space  represented  by  the  minute  fraction  *JL^fHTi  = 
0000001,  or  about  the  one  ten-millionth  part  of  one 
foot.  These  quantities  look  to  be  minute  and  quite 
unworthy  of  notice,  and  yet  from  these  small  disturbing 
effects,  accumulating  through  ages,  arise  all  the  amazing 
changes  which  are  progressing  among  the  elements  of  the 
planetary  orbits. 

We  will  not  extend  these  details,  but  refer  for  further 
particulars  to  the  Appendix. 

THE  ASTEROIDS  AS  PONDERABLE  BODIES. — As  yet  W6 

have  no  certain  knowledge  of  the  magnitude  or  masses 
of  these  minute  worlds.  We  are  assured  that  they  are 
subjected  to  the  laws  of  motion  and  gravitation,  and  that 
the  elements  of  their  orbits  are  undergoing  the  same 
modifications  to  which  the  elements  of  the  orbits  of  all 
the  planets  are  subjected.  These  planets  are  disturbed 
principally  by  the  action  of  Jupiter,  as  we  may  readily 
determine  by  an  examination  of  the  masses  and  distances 
of  the  two  nearest  planets,  inside  and  outside  the  orbits 
of  the  asteroids. 

The  mean  distance  of  the  group  from  the  sun  is  about 
2.5  times  the  earth's  distance.  The  distance  of  Mars,  in 
terms  of  the  same  unit,  is  1.5,  and  the  distance  of  Jupi- 
ter from  the  sun  is  5.2.  Hence,  from  the  mean  distance 
of  the  asteroids  to  Jupiter  is  5.2— 2.5=2.7,  and  from  the 


344  THE     SUN    AND    PLANETS 

same  to  Mars  is  2.5—1.5=1.0.  Hence,  if  Mars  and 
Jupiter  were  equal  in  weight,  the  power  of  Mars  over  the 
central  asteroid  would  exceed  the  power  of  Jupiter  in  the 
ratio  of  (2.7)2  to  (l.O)2,  or  in  the  ratio  of  7.3  to  1.  But 
Jupiter  is  2560  times  heavier  than  Mars,  and  hence  his 
power  will  be  increased  in  like  proportion,  and  the  at- 
traction of  Mars  will  be  to  that  of  Jupiter  as  7.3  to  2560, 
or  as  1  to  350  nearly.  Hence  we  perceive  that  Jupiter  13 
the  principal  disturber  in  the  movements  of  the  asteroids. 
For  further  particulars  the  reader  will  consult  the 
Appendix. 

JUPITER  AND  HIS  SATELLITES  AS  HEAVY  BODIES. — 
This  planet  is  not  only  heavier,  but  its  volume  is  much 
greater  than  that  of  any  one  of  the  planets.  Being  5.2 
further  from  the  sun  than  the  earth,  it  will  be  attracted 
by  a  power  diminished  in  the  ratio  of  the  square  of  5.2 
to  1,  or  as  27  to  1  nearly. 

The  weight  of  Jupiter  is  to  that  of  the  earth  as  338  to 
1,  and  in  case  his  diameter  were  exactly  equal  to  that  of 
the  earth,  a  body  weighing  one  pound  at  the  terrestrial 
equator  would  weigh  at  the  equator  of  this  planet  338 
pounds.  But  the  diameter  of  Jupiter  is  90,734  miles, 
and  its  radius  45,377  miles,  or  more  than  ten  times  the 
radius  of  the  earth.  His  attraction  on  a  body  upon  the 
surface  will  therefore  be  reduced  on  account  of  this  ten- 
fold distance  to  the  one  hundredth  of  338  pounds,  or  to 
3.38  pounds,  or,  if  the  computation  be  made  precisely, 
the  result  gives  us  2.81  as  the  weight  of  one  terrestrial 
pound  at  the  equator  of  this  planet.  The  student  can 
compute  the  reduction  in  the  gravity  of  the  planet  at  the 
equator  arising  from  the  action  of  the  centrifugal  force, 
the  planet  revolving  on  its  axis  in  9h.  55m.  27s. 

The  principal  disturber  of  Jupiter  is  the  planet  Saturn. 


AS    PONDERABLE    BODIES.  345 

From  the  sun  to  Jupiter  is  5.2,  the  earth's  distance  being 
1.  From  Jupiter  to  Saturn  the  distance  is  4. 3  in  the 
same  terms.  Hence,  if  Saturn  weighed  as  much  as  the 
sun,  his  power  over  Jupiter  would  be  greater  in  the  ratio 
of  (5.2)'  to  (4.3)',  or  as  2T.04  to  18.44,  or  as  1.47  to  1. 
But  the  sun  weighs  as  much  as  3,502  Saturns,  and  hence 
his  power  over  Jupiter  will  exceed  that  of  Saturn  in  flie 
ratio  of -V.TT  **>  1,  or  as  2,380  to  1.  This,  of  course, 
is  the  ratio  of  the  forces  when  the  planets  are  in  con- 
junction. When  in  opposition  the  interval  between  them 
is  increased  by  the  diameter  of  the  orbit  of  Jupiter,  or 
by  10.4,  and  thus  it  becomes  14.7,  instead  of  4.3,  and 
in  this  position  the  disturbing  power  of  Saturn  is  reduced 
in  the  ratio  of  (14.7)a  to  (4.3)',  or  as  216.09  to  18.44, 
or  as  12  to  1. 

We  have  already  seen  how  we  can  ascertain  the  weight 
of  this  planet  by  observing  the  period  of  revolution  of 
his  satellites  and  by  measuring  their  distances.  By  tak- 
ing these  quantities  from  the  table  in  the  Appendix  the 
student  may  compute  readily  the  mass  of  Jupiter  as  com- 
pared with  that  of  the  earth. 

The  eccentricity  of  the  orbit  of  this  planet  amounts  to 
0.0481,  the  semi-major  axis  being  unity,  or  the  distance 
from  the  center  of  tHe  ellipse  to  the  focus  is  equal 
to  (242,500,000)  x  0.0481=11,664,250  miles.  This 
quantity  is  now  slowly  increasing,  and  gains  every  year 
in  length  388  miles.  This  is  due  to  the  disturbing  in- 
fluence of  the  surrounding  planets,  and  after  an  immense 
period  will  reach  a  limit  beyond  which  it  cannot  pass. 
The  increment  will  then  be  converted  into  decrement, 
and  a  limit  being  again  reached,  the  orbit  in  its  figure 
thus  oscillates  between  these  limits  in  calculable,  but  (so 
far  as  I  know)  in  periods  not  yet  calculated. 

15* 


346  THE    STJN    AND    PLANETS 

The  same  fact  is  true  of  the  inclination  of  the  plane 
of  Jupiter's  orbit  to  that  of  the  ecliptic.  On  the  1st 
January,  1840,  this  inclination  amounted  to  1°  IS'  42".4. 
Its  present  annual  decrease  is  O'^S,  and  should  this  con- 
tinue, at  the  end  of  about  200,000  years  these  planes 
would  coincide.  This,  however,  can  never  take  place 
The  decrease  finally  comes  to  be  converted  into  increase, 
and  thus  the  plane  of  the  orbit  of  Jupiter  may  be  said  to 
rock  to  and  fro  on  the  plane  of  the  ecliptic  in  periods 
reaching  to  even  millions  of  years. 

We  have  already  noticed  a  source  of  perturbation  in 
the  case  of  Venus  and  the  earth,  arising  from  the  ap- 
proximate commensurability  of  the  periods  of  revolution 
of  these  planets.  A  like  equation,  as  it  is  called,  exists 
in  the  case  of  Jupiter  and  Saturn.  Five  periods  of  Jupi- 
ter are  21,663,  and  two  of  Saturn's  periods  are  21,519 
days ;  so  that  in  case  the  planets  start  at  any  given  time 
from  a  conjunction,  at  the  end  of  five  revolutions  of  Jupi- 
ter and  two  of  Saturn,  the  planets  will  return  to  nearly 
the  same  points  of  their  orbits  and  to  the  same  relative 
positions.  But  the  synodical  period,  or  the  time  from 
conjunction  to  conjunction  of  these  planets  is  7,253.4 
days,  and  three  times  this  quantity  amounts  to  21,760.2. 
Hence  we  perceive  Jupiter  in  this  period  will  have  per- 
formed five  revolutions  and  21,760—21,663=97  days 
over,  while  Saturn  will  describe  two  revolutions  and  240 
days  over,  and  during  these  excesses  the  planets  advance 
in  their  respective  orbits  8°  6'.  Thus  every  third  con- 
junction will  fall  8°  6'  in  advance  of  the  former  one,  and 
the  conjunction  line  will  be  thus  carried  round  the  entire 
orbit  in  about  44  times  x  21, 760  days,  or  in  2,648 
years,  at  the  end  of  which  cycle  the  same  exact  condition 
will  be  restored,  and  all  the  perturbations  in  the  same 


AS    PONDERABLE    BODIES.  347 

time  completely  obliterated,  provided  the  figures  of  the 
orbits  remain  unchanged.  Indeed,  a  restoration  is  effected 
partially  and  almost  completely  in  consequence  of  the 
triple  conjunction  which  takes  place  in  the  period  of 
21,760  days.  These  conjunctions  fall  at  points  on  the 
orbits  120°  apart,  and  thus  tend  to  effect  a  restoration, 
which  is  only  fully  perfected,  however,  at  the  end  of  the 
great  cycle  of  2,648  years. 

Here  we  find  again  the  cause  which  prevents  the  laws 
of  Kepler  from  being  rigorously  applicable  to  the  planet- 
ary movements.  In  case  Jupiter  existed  alone,  then  the 
line  drawn  from  the  planet  to  the  sun  would  sweep  over 
equal  areas  in  equal  times,  as  it  is  carried  by  the  planet 
around  the  sun.  But  the  association  of  the  two  planets 
renders  the  application  of  this  law  no  longer  possible. 
Jupiter  is  dragged  back  by  Saturn,  and  Saturn  is  dragged 
forward  by  Jupiter  when  they  start  off  from  their  line 
of  conjunction ;  but  here  comes  in  a  most  wonderful 
compensation  in  the  fact  that  whatever  Jupiter's  motion 
loses  by  the  disturbing  influence  of  Saturn,  Saturn's  mo- 
tion gains  by  the  disturbing  influence  of  Jupiter.  So 
that  the  sum  of  the  areas  swept  over  by  the  lines  joining 
the  two  planets  with  the  sun  will  always  be  equal  in 
equal  times. 

We  shall  not  extend  further  our  notices  of  the  results 
arising  from  the  action  of  gravitation  on  the  planets  and 
their  satellites  —having  discussed  to  some  extent  the 
mutual  perturbations  of  Uranus  and  Neptune  in  a  former 
chapter. 

We  will  close  by  an  extension  of  the  principle  laid 
down  in  the  case  of  Jupiter  and  Saturn  to  the  entire 
planetary  system.  If  at  any  moment  lines  were  drawn 
from  the  center  of  the  sun  to  each  of  the  planets  in  the 


348  THE     SUN    AND     PLANETS. 

entire  system,  and  from  the  center  of  each  of  the  planets 
to  their  respective  satellites,  the  areas  swept  over  by  all 
these  lines  thus  drawn  will  always  be  equal  in  equal 
times.  Thus,  while  not  a  solitary  planet  or  satellite  can 
follow  this  law  of  equal  areas,  the  combined  scheme  is 
bound  by  it  in  the  most  rigorous  manner ;  and  if  the 
amount  of  area  described  by  the  entire  system  in  one 
hour  were  determined  to-day,  and  be  sent  down  to  pos- 
terity, at  the  end  of  ten  thousand  years,  a  like  computa- 
tion being  made,  the  same  identical  result  will  be  reached, 
provided  the  system  remain  free  from  any  disturbing  in- 
fluence exterior  to  itself. 

In  case,  therefore,  the  sun  with  all  his  planets  and 
comets  is,  indeed,  drifting  through  space  into  other  stellar 
regions,  the  time  may  come  when  the  fixed  stars  may  so 
disturb  the  sum  of  the  areas  as  to  point  out  clearly  the 
fact  that  our  system  has  positively  changed  its  location 
in  space. 

We  will  close  our  discussion  of  the  sun  and  his  satel- 
lites by  the  examination  of  an  hypothesis  which  has  been 
propounded  to  account  for  the  peculiar  organization  of 
this  vast  scheme  of  revolving  worlds. 


CHAPTER    XVI. 


THE     NEBULAR     HYPOTHESIS. 


THE   ARRANGEMENT   OF  THE   SOLAR   SYSTEM.— THE   PHENOMENA  FOR 

GRAVITATION  is  RESPONSIBLE.— THE  PHENOMENA  REMAINING  TO  BE  Ao- 
COUNTED  FOR.— NEBULOUS  MATTER  AS  FOUND  IN  COMETS.— NEBULOUS  MAT- 
TER POSSIBLY  nr  THE  HEAVENS.— THE  ENTIRE  SOLAR  SYSTEM  ONCE  A 
GLOBE  OF  NEBULOUS  MATTER. — Monow  OF  ROTATION. — RADIATION  of 
HEAT. — CONDENSATION  AND  ITS  EFFECTS. — RINGS  DISENGAGED  FROM  THB 
EQUATOR  OF  THE  REVOLVING  MASS.— FORMATION  OF  PLANETS  AND  OF 
SATELLITES. 

IN  our  examination  of  the  scheme  of  worlds  which  re- 
volve around  the  sun  we  have  found  that  the  orbits  of  the 
planets  are  all  nearly  circular,  that  their  planes  are  all 
nearly  coincident  with  the  plane  of  the  ecliptic,  and  that 
this  plane  is  nearly  coincident  with  the  plane  of  the  sun's 
equator ;  that  the  planets  all  revolve  in  the  same  direc- 
tion around  the  sun,  and  that  the  sun  and  planets  and 
satellites  all  rotate  on  their  axes  in  the  same  direction ; 
that  the  periods  of  revolution  grow  shorter  in  the  planets 
and  satellites  as  their  distances  from  their  primary  grow 
less ;  that  the  sun  rotates  on  his  axis  in  a  shorter  period 
than  that  employed  in  the  revolution  of  any  planet ;  that 
every  planet  accompanied  by  satellites  rotates  on  its  axis 
in  a  less  time  than  the  period  of  revolution  of  any  satel- 
Kte.  The  law  of  gravitation  is  not  responsible  for  any 
of  these  facts,  and  in  case  we  compute  the  chances  of  such 
an  organization  coming  into  being  by  accident,  we  shall 


350          THE    NEBULAR    HYPOTHESIS. 

find  but  one  chance  in  so  many  millions  that  we  are 
compelled  to  look  to  some  higher  cause  than  mere  acci- 
dent to  account  for  so  great  a  multitude  of  combined 
phenomena. 

We  have  said  that  gravitation  is  not  responsible  for 
the  facts  above  stated.  In  case  a  solitary  planet  be  pro- 
jected with  a  given  force,  and  in  a  given  direction  about 
the  sun,  and  at  a  given  distance,  it  will  revolve,  as  we 
have  seen,  in  one  of  four  curves,  and  in  any  one  of  these 
curves  it  will  be  held  equally  by  the  law  of  gravitation. 
The  plane  in  which  it  revolves  may  assume  any  angle 
with  a  fixed  plane,  the  direction  of  the  revolution  may  be 
the  same  or  contrary  to  that  in  which  the  sun  rotates,  the 
orbit  may  be  a  circle,  an  ellipse,  a  parabola,  or  an  hyper- 
bola, and  yet  the  planet  shall  revolve,  subject  to  the  law 
of  gravitation.  It  may  rotate  on  its  own  axis  either  with 
or  against  its  revolution  in  its  orbit,  and  in  case  we  give 
to  this  planet  a  satellite,  the  same  statements  are  true 
with  reference  to  this  attendant.  So  that,  so  far  as  the 
law  of  gravitation  is  concerned,  there  might  have  been 
among  the  planets  all  the  diversity  in  the  form  of  their 
orbits  in  the  angles  of  their  inclination  to  a  fixed  plane, 
and  in  the  direction  of  their  motions,  as  are  found  among 
the  comets,  and  yet  each  object  would  have  been  subject 
to  the  great  law  of  universal  gravitation. 

We  cannot,  therefore,  affirm  that  the  peculiar  struc- 
ture of  the  solar  system  results  from  the  laws  of  motion 
and  gravitation,  without  pre-supposing  a  condition  of 
matter  entirely  different  from  that  now  recognized  as  ex- 
isting in  the  planets  and  their  satellites.  We  have  already 
noticed  the  wonderful  constitution  of  the  comets.  In 
these  bodies  is  found  a  kind  of  matter  which  has  been 
termed  nebulous,  in  which  the  minute  particles  are  sepa- 


THE    1TEBULAR    HYPOTHESIS.          351 

rated  by  some  repulsive  force,  and  the  entire  mass  is  but 
a  vapor  of  the  most  refined  tenuity. 

Among  the  stellar  regions  the  telescope  has  revealed 
objects  whose  light  is  so  faint  and  whose  forms  are  so  ill 
defined  that  they  have  been  regarded  by  many  astrono- 
mers of  high  reputation  to  be  analogous  to  the  comets  in 
their  material,  exhibiting  the  primitive  or  primordial  con- 
dition of  the  matter  composing  the  physical  universe. 
This  conjecture  (for  it  is  nothing  more)  may  be  true  or 
false,  but  its  truth  or  falsehood  cannot  in  any  way  affect 
the  credibility  of  the  theory  or  hypothesis  we  are  about 
to  present.  The  present  condition  of  matter  cannot  in 
any  way  be  assumed  to  be  the  only  condition  in  which  it 
ever  existed,  since  we  now  know  it  to  be  subject  to  extra- 
ordinary changes  and  most  wonderful  modifications. 

Let  us,  then,  suppose  that  a  time  once  was  when  the 
sun  and  all  its  planets  and  their  satellites  existed  as  one 
mighty  globe  of  nebulous  matter,  whose  diameter  far  ex- 
ceeded the  present  diameter  of  the  orbit  of  Neptune,  that 
to  this  stupendous  globe  a  motion  of  rotation  was  given, 
and  that  its  heat  is  slowly  lost  by  radiation,  and  let  us 
endeavor  to  follow  the  changes  which  must  flow  from  the 
loss  of  heat  and  the  operation  of  the  laws  of  motion  and 
gravitation,  and  learn  whether  from  this  parent  mass  a 
scheme  of  planets  and  satellites  such  as  now  exist  can  be 
generated.  We  prefer  to  present  the  reasoning  in  the 
language  of  M.  Pontecoulent,  one  of  the  most  eminent 
of  the  illustrious  disciples  of  Newton — merely  premising 
that  in  case  the  central  rotating  mass  contracts  by  loss  of 
heat  that  a  time  must  come  when,  in  consequence  of  the 
increased  velocity  of  rotation,  the  force  of  gravity  of  a 
particle  at  the  equator  will  be  overcome  by  the  centrifu- 
gal force  generated  by  the  velocity  of  rotation,  and  hence 


THE    NEBULAE    HYPOTHESIS. 

flat  zones  or  rings  of  vapor  or  nebulous  matter  must 
eventually  be  formed  in  the  plane  of  the  equator  of  the 
revolving  globe : — 

"  These  zones  must  have  begun  by  circulating  round 
the  sun  in  the  form  of  concentric  rings,  the  most  volatile 
molecules  of  which  have  formed  the  superior  part,  and 
the  most  condensed  the  inferior  part.  If  all  the  nebulous 
molecules  of  which  these  rings  are  composed  had  con- 
tinued to  cool  without  disuniting,  they  would  have  ended 
by  forming  a  liquid  or  solid  ring.  But  the  regular  con- 
stitution which  all  parts  of  the  ring  would  require  for 
that,  and  which  they  would  have  needed  to  preserve 
whilst  cooling,  would  make  this  phenomenon  extremely 
rare.  Accordingly  the  solar  system  presents  only  one 
instance  of  this,  that  of  the  rings  of  Saturn.  Generally 
the  ring  must  have  broken  into  several  parts,  which  have 
continued  to  circulate  round  the  sun,  and  with  almost 
equal  velocity,  while  at  the  same  time,  in  consequence  of 
their  separation,  they  would  acquire  a  rotatory  motion 
round  their  respective  centers  of  gravity;  and  as  the 
molecules  of  the  superior  part  of  the  ring,  that  is  to  say, 
those  furthest  from  the  center  of  the  sun,  had  necessarily 
an  absolute  velocity  greater  than  the  molecules  of  the  in- 
ferior part  which  is  nearest  it,  the  rotatory  motion,  com- 
mon to  all  the  fragments,  must  always  have  been  in  the 
same  direction  as  the  orbitual  motion. 

"  However,  if  after  their  division  one  of  these  frag- 
ments has  been  sufficiently  superior  to  the  others  to  unite 
them  to  it  by  its  attraction,  they  will  have  formed  only  a 
mass  of  vapor,  which,  by  the  continual  friction  of  all  its 
parts,  must  have  assumed  the  form  of  a  spheroid  flattened 
at  the  poles  and  elongated  in  the  direction  of  its  equator. 
Here,  then,  are  rings  of  vapor  left  by  the  successive  re- 


THE    NEBULAR    HYPOTHESIS.          353 

treats  of  the  atmosphere  of  the  sun,  changed  into  so  many 
planets  in  the  condition  of  vapor  circulating  round  the 
sun,  and  possessing  a  rotatory  motion  in  the  direction  of 
their  revolution.  This  must  have  been  the  most  common 
case  ;  but  that  in  which  the  fragments  of  some  ring  would 
form  several  distinct  planets  possessing  degrees  of  velo- 
city must  also  have  taken  place,  and  the  telescopic  plan- 
ets discovered  during  the  present  century  seem  to  present 
an  instance  of  this ;  at  least  if  it  is  not  admitted  with 
Olbers,  that  they  are  the  fragments  of  a  single  planet, 
broken  by  a  strong  interior  commotion.  It  is  easy  to 
imagine  the  successive  changes  produced  by  cooling  on 
the  planets  whose  formation  has  been"  just  pointed  out. 
Indeed,  each  of  these  planets,  in  the  condition  of  vapor, 
is,  in  every  respect,  like  one  of  the  nebula  in  the  first 
stage ;  they  must,  therefore,  before  arriving  at  a  state  of 
solidity,  pass  through  all  the  stages  of  change  we  have 
just  traced  in  the  sun.  At  first  the  condensation  of  their 
atmosphere  will  form  round  the  center  of  the  planet  a 
body  composed  of  layers  of  unequal  density,  the  densest 
matter  having,  by  its  weight,  approached  the  center, 
and  the  most  volatile  reached  the  surface,  as  we  see  in 
a  vessel  different  liquids  ranged  one  above  another,  ac- 
cording to  their  specific  gravity  to  arrive  at  a  state  of 
equilibrium.  The  atmosphere  of  each  planet  will,  like 
that  of  the  sun,  leave  behind  it  zones  of  vapor,  which  will 
form  one  or  several  secondary  planets,  circulating  round 
the  principal  planet  as  the  moon  does  round  the  earth, 
and  the  satellites  round  Jupiter,  Saturn,  and  Uranus,  or 
else  they  will  form,  by  cooling  without  dividing,  a  solid 
and  continuous  circle,  of  which  we  have  an  instance  in 
the  ring  of  Saturn.  In  every  case  the  direction  of  the 
rotatory  and  orbitual  motion  of  the  satellites  or  the  ring 


354          THE    NEBULAR    HYPOTHESIS. 

will  be  the  same  as  that  of  the  rotatory  motion  of  the 
planet;  and  this  is  completely  confirmed  by  observation. 

"The  wonderful  coincidence  of  all  the  planetary  mo- 
tions, (a  phenomenon  which  we  cannot,  without  infringing 
the  laws  of  probability,  regard  as  merely  the  effect  of 
chance,)  must  then  be  the  result  even  of  the  formation  of 
the  solar  system  on  this  ingenious  hypothesis ;  we  see 
also  why  the  orbits  of  the  planets  and  satellites  are  so 
little  eccentric,  and  deviate  so  little  from  the  plane  of 
the  solar  equator.  A  perfect  harmony  between  the 
density  and  temperature  of  their  molecules  in  a  state  of 
vapor  would  have  rendered  the  orbits  rigorously  circular 
and  made  to  coincide  with  the  plane  of  this  equator ;  but 
this  regularity  could  not  exist  in  all  parts  of  such  large 
masses  ;  there  has  resulted  the  slight  eccentricities  of  the 
orbits  of  the  planets  and  satellites,  and  their  deviation 
from  the  plane  of  the  solar  equator. 

"  When  in  the  zones  abandoned  by  the  solar  atmosphere 
there  are  found  molecules  too  volatile  either  to  unite  with 
each  other  or  with  the  planets,  they  must  continue  to 
revolve  round  the  sun,  without  offering  any  sensible  re- 
sistance to  the  motions  of  the  planetary  bodies,  either  on 
account  of  their  extreme  rarity,  or  because  their  motion 
is  effected  in  the  same  way  as  that  of  the  bodies  they  en- 
counter. These  wandering  molecules  must  thus  present 
all  the  appearances  of  the  zodiacal  light. 

"  We  have  seen  that  the  figure  of  the  heavenly  bodies 
was  the  necessary  result  of  their  fluidity  at  the  begin- 
ning of  time.  The  singular  phenomenon  presented  by 
the  rigorous  equality  indicated  by  observation  among  the 
lesser  motions  of  rotation  and  revolution  of  each  satel- 
lite, an  equality  rendering  the  opposed  hemisphere  of  the 
moon  forever  invisible  to  us,  is  another  obvious  conse- 


THE    NEBULAE     HYPOTHESIS.          355 

quence  of  this  hypothesis.  Indeed,  supposing  that  the 
slightest  difference  had  existed  between  the  mean  motion 
of  rotation  and  revolution  of  our  satellite  while  it  was  in 
the  state  of  vapor  or  of  fluidity,  the  attraction  of  the 
earth  would  have  elongated  the  lunar  spheroid  in  the 
direction  of  its  axis  towards  the  earth.  The  same  attrac- 
tions would  have  tended  to  diminish  insensibly  the  differ- 
ence between  the  rotatory  and  orbitual  motions  of  the 
moon,  so  as  to  confine  to  narrow  limits  a  condition 
sufficient  to  cause  the  axis  of  its  equator,  directed 
towards  the  earth,  to  be  subject  only  to  a  species  of 
periodical  balancing  constituting  the  phenomenon  of  libra- 
tion.  If  these  oscillations  are  not  now  observed,  it  is  be- 
cause they  have  ceased  to  exist  in  consequence  of  the 
resistance  they  have  encountered  in  the  course  of  time, 
even  as  the  oscillations  of  the  terrestrial  axis  in  the  in- 
terior of  the  earth,  arising  from  the  initial  state  of  mo- 
tion, have  been  destroyed,  and  as  indeed  all  the  motions 
of  the  heavenly  bodies  have  disappeared  which  have  not 
had  a  permanent  cause. 

"  The  principal  phenomena  of  the  planetary  system 
are  therefore  explained  with  great  facility  by  the  hypo- 
thesis we  are  examining ;  and  as  these  successive  changes 
of  a  nebulous  mass  and  the  leaving  of  a  part  of  its 
substance  by  cooling,  agree  with  all  the  leading  pheno- 
mena, it  must  be  allowed  a  high  degree  of  probability. 
In  this  hypothesis  the  formation  of  the  planets  would  not 
have  been  simultaneous  ;  they  have  been  created  succes- 
sively at  intervals  of  ages ;  the  oldest  are  those  which 
are  furthest  from  the  sun,  and  the  satellites  are  of  a 
more  recent  date  than  their  respective  planets.  It  may 
be,  if  we  are  ever  permitted  to  reach  so  high,  that  by 
an  examination  of  the  constitution  of  each  planet  we  may 


356          THE     NEBULAR    HYPOTHESIS. 

go  back  to  the  epoch  of  its  formation,  and  assign  to  each 
its  place  in  the  chronology  of  the  universe.  It  is  like- 
wise seen  that  the  velocity  of  the  orbitual  motion  of  each 
planet,  as  it  is  now,  must  differ  little  from  that  of  the 
rotatory  motion  of  the  sun  at  the  period  when  the  planet 
was  detached  from  its  atmosphere.  And  as  the  rotatory 
motion  is  accelerated  in  proportion  as  the  solar  molecules 
are  confined  by  cooling,  so  that  the  sum  of  the  areas 
which  they  describe  round  the  center  of  gravity  would 
remain  always  the  same,  it  follows  revolutionary  motion 
must  be  so  much  more  rapid  as  the  planet  is  nearer  the 
sun,  as  is  seen  by  observation.  It  likewise  results  that 
the  duration  of  the  rotation  either  of  the  sun  or  of  a 
planet  must  be  shorter  than  the  duration  of  the  nearest 
body  which  circulates  round  them  •  this  observation  is 
completely  confirmed  even  in  those  cases  where  the  differ- 
ence between  the  duration  of  the  two  motions  must  be 
very  slight.  Thus  the  interior  ring  of  Saturn  being 
very  close  to  the  planet,  the  duration  of  its  rotation  must 
be  almost  equal,  but  a  little  longer  than  that  of  the 
planet. 

"  The  observations  of  Herschel  give,  indeed,  0.432 
as  the  duration  of  the  rotation  of  the  ring,  and  0.427  as 
that  of  the  planet ;  why,  then,  should  we  not  admit  that 
this  ring  has  been  formed  by  the  condensation  of  the  at- 
mosphere of  Saturn,  which  formerly  extended  to  it? 
We  may  perhaps  deduce  from  the  laws  of  mechanics  and 
the  actual  dimensions  of  the  ?sun,  and  the  known  dura- 
tion of  its  rotation,  the  relation  existing  between  the 
radius  vector  of  its  surface  and  the  time  of  its  rotation 
in  the  different  stages  of  concentration  through  which  it 
has  passed.  The  third  law  of  Kepler  would  be  no 
longer  the  mere  result  of  observation ;  it  would  be  di- 


TH2    NEBULAR    HYPOTHESIS.          357 

rectly  deduced  from  the  primordial  laws  of  the  heavenly, 
bodies. 

"In  this  system  the  particular  form  of  the  planets, 
the  flattening  at  the  poles,  and  bulging  out  at  the  equa- 
tor, is  only  the  necessary  consequence  of  the  laws  of  the 
equilibrium  of  fluids,  and  easily  explains  the  greater  part 
of  the  phenomena  observed  by  geologists  in  the  consti- 
tution of  the  terrestrial  globe,  which  appear  inexplicable, 
if  it  is  not  admitted  that  the  earth  and  planets  have  been 
originally  fluid. 

"  Let  us  now  see  what  is  the  origin  and  part  assigned 
to  comets  by  this  hypothesis.  La  Place  supposes  that 
they  do  not  belong  to  the  planetary  system,  and  he  re- 
gards them  as  masses  of  vapor  formed  by  the  agglomera- 
tion of  the  luminous  matter  diffused  in  all  parts  of  the 
universe,  and  wandering  by  chance  in  the  various  solar 
systems.  Comets  would  thus  be,  in  relation  to  the  plan- 
etary system,  what  the  aerolites  are  in  relation  to  the 
earth,  with  which  they  seem  to  have  no  original  con- 
nection. When  a  comet  approaches  sufficiently  near  the 
regions  of  space  occupied  by  our  system  to  enter  into  the 
sphere  of  the  sun's  influence,  the  attraction  of  that 
luminary,  combined  with  the  velocity  acquired  by  the 
comet,  causes  it  to  describe  an  elliptic  or  hyperbolic 
orbit.  But  as  the  direction  of  this  velocity  is  quite  arbi- 
trary, comets  must  move  in  every  direction  and  in  every 
part  of  the  sky. 

"  The  cometary  orbits  will,  then,  have  every  inclina- 
tion to  the  ecliptic ;  and  this  hypothesis  explains  equally 
well  the  great  eccentricity  by  -which  they  are  usually 
effected.  Indeed,  if  the  curves  described  by  comets  are 
ellipses,  they  must  be  greatly  elongated,  since  their 
major  axes  are  at  least  equal  to  the  radius  of  tho 


358          1HE    NEBULAE    HYPOTHESIS. 

sphere  of  the  sun's  attraction;  and  we  must  conse- 
quently be  able  to  see  only  those  whose  eccentricity  is 
very  great,  and  perihelion  distance  inconsiderable  ;  all 
others,  on  account  of  their  minuteness  and  distance, 
must  always  be  invisible,  unless  at  least  the  resistance 
of  the  ether,  the  attraction  of  the  planets,  or  other  un- 
known ca,uses  diminish  their  perihelion  distance,  and 
bring  them  nearer  the  terrestrial  orbit.  The  same  cir- 
cumstances may  change  the  primitive  orbits  of  some 
comets  into  ellipses,  whose  major  axes  are  comparatively 
small ;  and  this  has  probably  happened  to  the  periodi- 
cal comets  of  1759,  1819,  and  1832.  The  laws  of  the 
curvilinear^  motion  likewise  show  that  the  eccentricity 
of  the  orbit  chiefly  depends  on  the  direction  of  the 
comet's  motion  on  its  entering  the  sphere  of  the  sun's 
attraction  ;  and  as  this  motion  is  possible  in  every  di- 
rection, there  are  no  limits  to  the  eccentricities  of  the 
orbits  of  comets. 

"  If,  at  the  formation  of  the  planets,  some  comets 
penetrated  the  atmospheres  of  the  sun  and  planets,  the 
resistance  they  met  would  gradually  destroy  their  ve- 
locity ;  they  would  then  fall  on  those  bodies  describing 
spirals,  and  their  fall  would  have  the  effect  of  causing 
the  planes  of  the  orbits  and  equators  of  the  planets  to 
remove  from  the  plane  of  the  solar  equator.  It  is, 
therefore,  partly  to  this  cause,  and  partly  to  those  we 
have  developed  above,  that  the  slight  deviations  we  now 
perceive  must  be  attributed. 

"  Such  is  a  summary  of  the  "hypothesis  of  La  Place  on 
the  origin  of  the  solar  system.  This  hypothesis  ex- 
plains, in  the  most  satisfactory  manner,  the  three  most 
remarkable  phenomena  presented  by  the  planetary  mo- 
tions. 


THE    NEBULAR    HYPOTHESIS.          359 

"  1st  The  motioL  of  the  planets  in  the  same  direction, 
and  nearly  in  the  same  plane. 

"  2d.  The  motion  of  the  satellites  in  the  sams  direction 
as  their  planets. 

"  3d.  The  singular  coincidence  in  direction  of  the  ro- 
tatory and  orbitual  motions  of  the  planets  and  the  sun, 
•which  in  other  systems  would  present  inexplicable  diffi- 
culties. 

"  The  no  less  remarkable  phenomena  of  the  smallness 
of  the  eccentricities  and  inclinations  of  the  planetary 
orbits  are  also  a  necessary  consequence  of  it,  while  we  see 
at  the  same  time  why  the  orbits  of  the  comets  depart 
from  this  general  law,  and  may  be  very  eccentric,  and 
have  any  inclination  whatever  to  the  ecliptic.  The  flat- 
tening of  the  form  of  the  planets,  shown  on  the  earth  by 
the  enlargement  of  degrees  of  the  meridian,  and  by  the 
regular  increase  of  weight  in  going  from  the  equator  to 
the  poles,  is  only  the  result  of  the  attraction  of  their  mole- 
cules while  they  were  yet  in  a  state  of  vapor,  combined 
with  the  centrifugal  force  produced  by  the  rotatory  mo- 
tion impressed  on  the  fluid  mass.  In  short,  among  the 
phenomena  presented  by  the  motions  and  the  form  of  the 
heavenly  bodies,  there  are  none  which  cannot  be  ex- 
plained with  extreme  facility  by  the  successive  condensa- 
tion of  the  solar  system ;  and  the  more  this  system  is 
examined  the  more  we  are  led  to  acknowledge  its  proba- 
bility. 

"  Undoubtedly,  if,  as  La  Place  has  himself  said,  a  hy- 
pothesis not  founded  on  observation  or  calculation  must 
always  be  presented  with  extreme  diffidence,  this,  it  will 
be  granted,  acquires,  at  least  by  the  union  and  agreement 
of  so  many  different  facts,  all  the  marks  of  probability. 
But  what,  in  my  opinion,  principally  distinguishes  it  from 


360  THE     NEBULAR    HYPOTHESIS. 

the  ordinary  theories  concerning  the  formation  of  systems, 
is  the  identity  which  it  establishes  between  the  solar  sys- 
tem and  the  stars  spread  so  profusely  through  the  sky. 

"  All  the  phenomena  of  nature  are  connected,  all  flow 
from  a  few  simple  and  general  laws,  and  the  task  of  the 
man  of  genius  consists  in  discovering  those  secret  connec- 
tions, those  unknown  relations  which  connect  the  pheno- 
mena which  appear  to  the  vulgar  to  have  no  analogy. 
In  going  from  a  phenomenon  of  which  the  primitive  law 
is  easily  perceived,  to  another  in  which  particular  cir- 
cumstances complicate  it  so  as  to  conceal  it  from  us,  he 
sees  them  all  flowing  from  the  same  source,  and  the 
secret  of  nature  becomes  his  possession.  Thus  the  laws 
of  the  elliptic  motion  of  the  planets  led  Newton  to  the 
great  principle  of  universal  gravitation,  which  he  would 
have  sought  for  in  vain  in  the  less  simple  phenomena  of 
the  rotatory  motion  of  the  earth,  or  the  flux  and  reflux 
of  the  sea.  But  this  great  principle  being  once  dis- 
covered, all  the  circumstances  of  the  planetary  motions 
were  explained,  even  in*  their  minutest  details,  and  the 
stability  of  the  solar  system  was  itself  only  the  necessary 
consequence  of  its  conformation,  without  which,  as  New- 
ton thought,  God  would  be  constantly  obliged  to  retouch 
his  work,  in  order  to  render  it  secure.  La  Place,  ex- 
tending to  all  the  stars,  and  consequently  to  the  sun,  the 
mode  of  condensation  by  which  the  nebula  are  changed 
into  stars,  has  connected  the  origin  of  the  planetary  sys- 
tem with  the  primordial  laws  of  motion,  without  recur- 
ring to  any  hypothesis  but  that  of  attraction.  He  has, 
therefore,  extended  to  the  fixed  stars  the  great  law  of 
universal  gravitation,  which  is  probably  the  only  efficient 
principle  of  the  creation  of  the  physical  world,  as  it  is  of 
its  preservation." 


THE    NEBULAR    HYPOTHESIS.          361 

Such  is  a  brief  outline  of  one  of  the  most  sublime 
speculations  that  has  ever  resulted  from  the  efforts  of 
human  thought.  It  carries  us  back  to  that  grand  epoch 
when  "  in  the  beginning  God  created  the  heavens  and  the 
earth,"  when  matter  was  first  called  into  being  in  its  un- 
formed nebulous  condition,  and  "  the  earth  was  without 
form  and  void,"  and  darkness  covered  the  mighty  deep 
of  unfathomable  space.  But  the  Spirit  of  God  moved  on 
the  boundless  flood  of  vaporous  matter  scattered  through 
the  dark  profound,  and  gave  to  each  particle  its  now 
eternal  function,  impressed  the  laws  of  gravitation  and 
motion,  selected  the  grand  centers  about  which  the  germs 
of  suns  and  systems  should  form,  and  in  infinite  wisdom 
drew  the  plan  of  that  one  scheme  which  we  have  at- 
tempted to  examine,  among  the  millions  that  shine  ia 
splendor  throughout  the  boundless  empire  of  space. 


APPENDIX. 


TABLES  OF  ELEMENTS. 

SOLAR   ELEMENTS,    EPOCH    1ST   JAN.,    1801. 

Mean  longitude 280°  39'  10".2 

Longitude  of  the  perigee 270°  30'  05".0 

Greatest  equation  of  center 1°  55'  27".3 

Decrease  of  same  in  one  year 0".173 

Inclination  of  axis  to  the  ecliptic. 82°  40'  00".0 

Motion  in  a  mean  solar  day 7°  30'  00".0 

Motion  of  perigee  in-365  days..., 1'  01".9 

Apparent  diameter 32'  12".6 

Mean  horizontal  parallax 8".6 

Rotation  in  mean  solar  hours 607h  48m  Os 

Time  of  passing  "over  one  degree  of  mean  longitude. . . .  24h  20m  58.1s 

Eccentricity  of  orbit  (semi-axis  major  1) 01685318 

Volume  (earth  as  1) 1415225 

Mass  (earth  as  1) 354936 

Mean  distance  in  miles 95,000,000 

Same  (earth's  radius  1) 23984 

Density  (earth  as  1) 0.250 

Diameter  hi  miles 888,646 

Gravity  at  equator. 28.7 

In  one  second  of  time  bodies  fall  hi  feet.. .  , .  462.07 


ELEMENTS  OF  THE  ORBIT  OF  MERCURY,  EPOCH  IST  JAN.,  1801. 

Mean  distance  from  the  sun  hi  miles. 36,725,000 

Same  (earth's  distance  as  1) „ .  .3870984 

Greatest  distance,  same  unit 4666927 

Least  distance,  same  unit , 3075041 

Eccentricity  (semi-axis  major  as  1) 2056178 


APPENDIX.  363 

Annual  variation  of  same  (increase) 0.000,000,03866 

Sidereal  revolution  in  days 87.9692824 

Synodical  revolution  in  days 115.877 

Longitude  of  perihelion  at  epoch 74°  57'  27".00 

Annual  variation  of  same  (increase) 5.81 

Longitude  of  ascending  node 46°  23'  55".00 

Annual  variation  of  same 10".07 

Inclination  of  orbit  to  ecliptic 7°  00'  13".30 

Annual  variation  of  same 00".  18 

Mean  daily  motion  in  orbit *. 245'  32'  .6 

Time  of  rotation  on  axis 24h  05m  28a 

Inclination  of  axis  to  ecliptic ^ Uncertain. 

Apparent  diameter '•  •  •  •  6".69 

Diameter  in  miles 3089 

"        (earth's  being  1) 0398 

Volume  (earth's  being  1) 0.0595 

Density  (earth's  being  1) 1.225 

Light  received  at  perihelion  (earth's  being  1) 10.58 

Same  at  aphelion  (earth's  being  1) 4.59 

"Weight  of  a  terrestrial  pound 0.48 

Space  fallen  through  in  one  second  of  time,  in  feet 7.70 

Mass  (earth's  as  1) 0.0769 


ELEMENTS  OF  VENUS  FOB  THE  1ST  JAN.,  1840. 

Mean  distance  from  the  sun  in  miles. 68,713,500 

Same  (earth's  distance  as  1) 7233317 

Greatest  distance,  same  unit 7282636 

Least  distance,  same  unit 7183998 

Eccentricity  (semi-axis  major  as  1) 0068183 

Annual  variation  of  same  (decrease) 0000006271 

Sidereal  revolution  in  days. 224.7007754 

Synodical  revolution  in  days. 583.920 

Longitude  of  the  perihelion 124°  14'  25".6 

Annual  variation  of  same  (decrease) 3".24 

Longitude  of  the  ascending  node 76°  11'  29".8 

Annual  variation  of  same  (decrease) 20".50 

Inclination  of  orbit  to  the  ecliptic 3°  23'  31".4 

Annual  variation  of  same  (increase) 0".07 

Mean  daily  motion  hi  orbit 96'  7".8 

Time  of  rotation  on  axis 23h  21m  21s 

Inclination  of  axis  to  the  ecliptic Uncertain 


364  APPENDIX. 

Apparent  diameter 17".10 

Diameter  in  miles 7,896 

Diameter  (earth's  being  1) 0.925 

Volume  (earth's  being  1) 9960 

Mass  or  weight  (earth's  being  1) 894 

Density  (earth's  being  1) 0.923 

Light  received  at  perihelion  (earth's  being  1) 1.94 

Same  at  aphelion  (earth's  being  1) 1.91 

'Weight  of  a  terrestrial  pound,  JOT  gravity 0.90 

Bpace  fallen  through  in  one  second  of  time,  in  feet 14.5 


ELEMENTS  OF  THE  EARTH,  1ST  JAN.,  1801. 

Mean  distance  in  miles 95,000,000 

Greatest  distance  (mean  distance  1) 1.0167751 

Least  distance,  same  unit 0.9832249 

Mean  sidereal  revolution  (solar  days) 365d  06h  09m  09s.6 

Mean  tropical  revolution 365d  05h  48m  49s.7 

Mean  annualistic  revolution 365d  06h  13m  49s.3 

Revolution  of  the  sun's  perigee  (solar  days). 7,645,793 

Mean  Longitude  (20"  for  aberration) 100°  39'  10".2 

Earth's  motion  in  perihelio  in  a  mean  solar  day. 1°  01'  09".9 

Mean  motion  in  a  solar  day 0°  59'  08".33 

Mean  motion  in  a  sidereal  day 0°  59'  58".64 

Motion  in  aphelion  in  a  mean  solar  day 0°  57'  11".50 

Mean  longitude  of  perihelion 99°  30'  05".0 

Annual  motion  of  perihelion  (east) 11".8 

Same  referred  to  the  ecliptic 1' 01".9 

Complete  tropical  revolution  of  same  in  years 20,984 

Obliquity  of  the  ecliptic 23°  27'  56".5 

Annual  diminution  of  same 0".457 

Nutation  (semi-axis  major) 9".4 

Precession  (annual) ;  luni-solar. 50".4 

Precession  in  longitude 50".l 

Complete  revolution  of  vernal  equinox  in  years 25, 868 

Lunar  nutation  in  longitude 17".579 

Solar  nutation  in  longitude 1".137 

Eccentricity  of  orbit  (semi-axis  major  1) 0.01678356 

Annual  decrease 0.0000004163 

Daily  acceleration  of  sidereal  over  mean  solar  time 3'  55".91 

From  vernal  equinox  to  summer  solstice. 92d  21h  50m 

From  summer  solstice  to  autumnal  equinox 93d  13h  44m. 


APPENDIX.  365 

From  autumnal  equinox  to  winter  solstice 89d  16h  44m 

From  winter  solstice  to  vernal  equinox 89d  Olh  33m 

Mass  (sun  as  1) 0.0000028173 

Density  (water  as  1) 5.6747 

Mean  diameter  in  miles 7916 

Polar,        "        «  7898 

Equatorial          «  7924 

Centrifugal  force  at  equator 0.00346 

Light  arrives  from  the  sun  in 8'  1 3".3 

Aberration..  .  20".25 


ELEMENTS  OF  THE  MOON.— EPOCH  1ST  JAN.,  1801. 

Mean  distance  from  the  earth  (earth's  radius  1) 60.273433 

Mean  sidereal  revolution  in  days. 27.321661 

Mean  synodical  revolution  in  days. 29.5305887 

Eccentricity  of  orbit 0.054908070 

Mean  revolution  of  nodes  in  days 6793.391080 

Mean  revolution  of  apogee  hi  days 3232.575343 

Mean  longitude  of  node  at  epoch 13°  53'  17".7 

Mean  longitude  of  perigee 266°  10'  07".5 

Mean  inclination  of  orbit 5°  08'  39".96 

Mean  longitude  of  moon  at  epoch 118°  17'08".3 

Mass  (earth  as  1) 0.011364 

Diameter  in  miles. 21646 

Density  (earth  as  1) 0.556 

Gravity  or  weight  of  one  terrestrial  pound 0.16 

Bodies  fall  in  one  second,  in  feet 2.6 

Diameter  (earth  as  1) 0.264 

Density  (water  as  1) 3.37 

Inclination  of  axis 1°30'10".8 

Maximum  evection. 1°  20'  29".9 

"         variation 35'42".0 

"         annual  equation 11' 12".0 

"         horizontal  parallax 1°01'24".0 

Mean  "  "        57'00".9 

Minimum  "  "        53'48".0 

Maximum,  apparent  diameter. 33'  31".l 

Mean  "  tt        31'07".0 

Minimum         "  "        29' 21".9 


366 


APPENDIX. 


ELEMENTS  OF  MARS  FOR  THE  1ST  JAN..  1840. 


Mean  distance  from  the  sun  in  miles 145,750,000 

Same  (earth's  distance  as  1) 1.523691 

Greatest  distance,  same  unit. 1.6657795 

Least  distance,  same  unit 1.3816025 

Eccentricity  (semi-axis  major  as  1) 0932528 

Annual  variation  of  same  (increase) 000009017  6 

Sidereal  revolution  in  days 686.9794561 

Synodical  revolution  in  days. 779.836 

Longitude  of  the  perihelion 333°  6'  38".4 

Annual  variation  of  same  (increase) 15".46 

Longitude  of  the  ascending  node 48°  16'  18".0 

Annual  variation  of  same  (decrease) 25".22 

Inclination  of  orbit  to  the  ecliptie 1°  51'  5".7 

Annual  variation  of  same  (decrease) 0".01 

Mean  daily  motion  in  orbit 31'  26".7 

Time  of  rotation  on  axis 24h  37m  22s 

Inclination  of  axis  to  the  ecliptic 59°  41'  49" 

Apparent  diameter. 5".8 

Diameter  in  miles 4,070 

Diameter  (earth's  being  1) 0.519 

Volume  (earth's  being  1) 1364 

Mass  or  weight  (earth's  being  1) 0.134 

Density  (earth's  being  1) 0.948 

Light  received  at  perihelion  (earth^  being  1) 524 

Same  at  aphelion  (earth's  being  1).. 360 

Weight  of  a  terrestrial  pound  or  gravity. 0.49 

Space  fallen  through  in  one  second  of  time,  in  feet 7,9 


APPENDIX. 


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APPENDIX.  369 


ELEMENTS  OP  JUPITER  FOR  THE  1ST  JAN.,  1540. 

Mean  distance  from  the  sun  in  miles 494,256,000 

Same  (earth's  distance  as  1) 5.202767 

Greatest  distance,  same  unit 5.453663 

Least  distance,  same  unit 4.951871 

Eccentricity  (semi-axis  mnjor  as  1). 0482235 

Annual  variation  of  same  (increase) 000001593 

Sidereal  revolution  in  days 4332.5848032 

Synodical  revolution  in  days 398.867 

Longitude  of  the  perihelion 11°  45'  32".8 

Ann^  variation  of  same  (increase) 6".65 

LongMde  of  the  ascending  node 98°  48'  37".8 

variation  of  same  (decrease) 15".90 

ion  of  orbit  to  the  ecliptic 1°  18'  42".4 

Annual  variation  of  same  (decrease) 0".23 

Mean  daily  motion  in  orbit. 4'  69".3 

Time  of  rotation  on  axis 9h  55m  26s 

Inclination  of  axis  to  the  ecliptic. 86<>  54'  30" 

Apparent  diameter 38".4 

Diameter  in  miles 92,164 

Diameter  (earth's  being  1) 11.225 

Yolume  (earth's  being  1) 1491. 

Mass  or  weight  (earth's  being  1) 342.738 

Density  (earth's  being  1) 0.238 

Light  received  at  perihelion  (earth's  being  1) 0408 

Same  at  aphelion  (earth's  being  1) 0336 

Weight  of  a  terrestrial  pound  or  gravity 2.45 

Space  fallen  through  in  one  second  of  time  in  feet 39.4 


ELEMENTS  OP  JUPITER'S  SATELLITES. 

NO.   1.  NO  ECCENTRICITY. 

Sidereal  revolution  hi  days Id  18h  27m  33.5063 

Mean  distance  (Jupiter's  radius  1). 6.04853 

Inclination  of  orbit  to  a  fixed  plane 0°  00'  00".0 

Inclination  of  this  plane  to  Jupiter's  equator 0°  00'  06".0 

Mass,  that  of  Jupiter  being  1,000,000,000 17328 

No.  2.  No  ECCENTRICITY. 

Sidereal  revolution  hi  days 3d  13h  14m  36.393a 

Mean  distance  (Jupiter's  radius  1). 9.62347 


370  APPENDIX 

Inclination  of  orbit  to  a  fixed  plane 0°  27'  50" 

Inclination  of  this  plane  to  Jupiter's  equator 0°  01'  05" 

Retrograde  revolution  of  nodes  on  fixed  plane  in  years  29.9142 
Mass,  Jupiter's  being  1,000,000,000 25235 

No.  3.  ECCENTRICITY  SMALL. 

Sidereal  revolution  in  days 7d  03h  42m  33.3623 

Mean  distance  (Jupiter's  radius  1) 15.35024 

Inclination  of  orbit  to  a  fixed  plane 0°  12'  20" 

Inclination  of  this  plane  to  Jupiter's  equator 0°  05'  02" 

Retrograde  revolution  of  nodes  on  fixed  plane  in  years  141.7390 

Ko.  4.  ECCENTRICITY  SMALL.  f 

Sidereal  revolution  in  days 16d  16h  31m  49p)2s 

Mean  distance  (Jupiter's  radius  being  1) 26.99835 

Inclination  of  orbit  to  a  fixed  plane 0°  1-^*8" 

Inclination  of  this  plane  to  Jupiter's  equator 0°  24W4" 

Retrograde  revolution  of  node  on  fixed  plane  in  years.  531,000 


ELEMENTS  OF  SATURN  FOR  THE  1ST  JAN.,  1840. 

Mean  distance  from  the  sun  in  miles 906,205,000 

Same  (earth's  distance  as  1) 9.538850 

Greatest  distance,  same  unit 10.073278 

Least  distance,  same  unit 9.004422 

Eccentricity  (semi-axis  major  as  1) 0560265 

Annual  variation  of  same  (decrease) 0.000003124 

Sidereal  revolution  in  days 10759.2197106 

Synodical  revolution  in  days 378.090 

Longitude  of  the  perihelion 89°  54'  41".2 

Annual  variation  of  same  (increase) 19".31 

Longitude  of  the  ascending  node 112°  16'  34".2 

Annual  variation  of  same  (decrease) 19".54 

Inclination  of  orbit  to  the  ecliptic 2°  29'  29".9 

Annual  variation  of  same  (decrease) 0".15 

Mean  daily  motion  in  orbit 2'  0".6 

Time  of  rotation  on  axis lOh  29m  17s 

Inclination  of  axis  to  the  ecliptic. 61°  49' 

Apparent  diameter 17".l 

Diameter  in  miles 75,070 

Diameter  (earth's  being  1) 9.022 

Volume  (earth's  being  1) 772.0 

Mass  or  weight  (earth's  being  1) 102.683 


APPENDIX.  371 

Density  (earth's  being  1) 0.138 

Light  received  at  perihelion  (earth's  being  1) 0123 

Same  at  aphelion  (earth's  being  1) 0099 

"Weight  of  a  terrestrial  pound  or  gravity 1.09 

Spaoe  fallen  through  in  one  second  of  time  in  feet 17.6 


ELEMENTS  OP  SATURN'S  SATELLITES. 
No.  1.  MIMAS. 

Sidereal  revolution  in  days Od  22h  37m  2T.9s 

Mean  distance  (Saturn's  radius  1) 3.3607 

Epoch 1790.0 

Mean  longitude  at  epoch 256°  58'  48" 

Eccentricity  and  Peri-Saturn i urn Unknown. 

Na  2.  ENCELADUS. 

Sidereal  revolution  in  days Id  08h  53m  06.7s 

Mean  distance  (Saturn's  radius  1) 4.3125 

Epoch 1836.0 

Mean  longitude  at  epoch 67°  41'  36" 

Eccentricity  and  Peri-Saturnium Unknown. 

No.  3.  TETHTS. 

Sidereal  revolution  in  days Id  21h  18m  25.7s 

Mean  distance  (Saturn's  radius  1) 5.3396 

Epoch 1836.0 

Mean  longitude  at  epoch 313°  43'  48" 

Eccentricity  and  Peri-Saturnium Uncertain. 

No.  4.  DIONB. 

Sidereal  revolution  in  days 2d  17h  41m  08.9s 

Mean  distance  (Saturn's  radius  1) 6.8398 

Epoch 1836.0 

Mean  longitude  at  epoch 327°  40'  48" 

Eccentricity  and  Peri-Saturnium Uncertain. 

No.  6.  RHEA, 

Sidereal  revolution  in  days 4d  12h  25m  10.8a 

Mean  distance  (Saturn's  radius  1) 9.5528 

Epoch 1836.0 

Longitude  at  epoch 353°  44'  00" 

Eccentricity  and  Peri-Saturnium Uncertain 

No.  6.  TITAN. 

Sidereal  revolution 15d  22h  41m  25.2s 

Mean  distance  (Saturn's  radius  1) 22.1451 


372  APPENDIX. 

Epoch 1830.0 

Mean  longitude  at  epoch 137°  21'  24" 

Eccentricity 0.02934 

Longitude  of  Peri-Saturnium 256°  38'  11" 

No.  7.  HYPERION. 

Sidereal  revolution 21d  07h  07m  40.8a 

Mean  distance  (Saturn's  radius  1) 26.7834 

Other  elements  unknown. 

Discovered  (Sept.  19,  1848,)  by  Bond  of  Cambridge,  and  by 
Lassell,  of  Liverpool 

No.  8.  JAPETUS. 

Sidereal  revolution 79d  7h  53m  40.4s 

Mean  distance  (Saturn's  radius  1) 64.3590 

Epoch 1790.0 

Mean  longitude  at  epoch 269°  37'  48" 

Eccentricity  and  Peri-Saturnium Unknown. 


ELEMENTS  OF  URANUS  FOR  THE  1ST  JAN,  1840. 

Mean  distance  from  the  sun  in  miles 1,822,328,000 

Same  (earth's  distance  as  1) 19.18239 

Greatest  distance,  same  unit 20.07630 

Least  distance,  same  unit 18.28848 

Eccentricity  (semi-axis  major  as  1) 0466006 

Annual  variation  of  same Unknown. 

Sidereal  revolution  in  days 30686.8205556 

Synodical  revolution  in  days 369.656 

Longitude  of  the  perihelion 168°  5'  24" 

Annual  variation  of  same  (increase) 2".28 

Longitude  of  the  ascending  node 73°  8'  47".8 

Annual  variation  of  same  (decrease) 36".05 

Inclination  of  orbit  to  the  ecliptic 0°  46'  29".2 

Annual  variation  of  same  (increase) 0".03 

Mean  daily  motion  in  orbit 42".4 

Time  of  rotation  on  axis Unknown. 

Inclination  of  axis  to  the  ecliptic Unknown. 

Apparent  diameter 4".l 

Diameter  in  miles , 36,216 

Diameter  (earth's  being  1) 4.344 

Yolume  (earth's  being  1) 86.5 

Mass  or  weight  (earth's  being  1) 17.55} 


APPENDIX.  373 

Density  (earth's  being  1) , 0.180 

Light  received  at  perihelion  (earth's  being  1) 0027 

Same  at  aphelion  (earth's  being  1) 0025 

Weight  of  a  terrestrial  pound  or  gravity 0.76 

Space  fallen  through  in  one  second  of  time,  in  feet 12.3 


ELEMENTS  OP  URANUS'  SATELLITES. 

No.  1.  ARIEL. 

Sidereal  revolution  in  days 2d  12h  29m  20.66s 

Mean  distance 7.40 

No.  2.  UMBRTEL. 

Sidereal  revolution  in  days 4d  3h  28m  8.00s 

Mean  distance 10.31 

NO.  3.  TlTANIA. 

Sidereal  revolution  in  days 8d  16h  56m  31.30s 

Mean  distance 16.92 

No.  4.  OBEBON. 

Sidereal  revolution  in  days 13d  llh  7m  12.6s 

Mean  distance .  22.56 


ELEMENTS  OF  NEPTUNE  FOB  THE  Isr  JAN.,  1854. 

Mean  distance  from  the  sun  in  miles 2,853,420,000 

Same  (earth's  distance  as  1) 30.03627 

Greatest  distance,  same  unit 30.29816 

Least  distance,  same  unit 29.77438 

Eccentricity  (semi-axis  major  as  1) 0087 183 

Annual  variation  of  same Unknown. 

Sidereal  revolution  in  days I 60126.722 

Synodical  revolution  in  days 367.488 

Longitude  of  the  perihelion 47°  17'  58" 

Annual  variation  of  same Unknown. 

Longitude  of  the  ascending  node 130°  10'  12" .3 

Annual  variation  of  same Unknown. 

Inclination  of  orbit  to  the  ecliptic 1°  46'  59".0 

Annual  variation  of  same Unknown, 

Mean  daily  motion  in  orbit 21".6 

Time  of  rotation  on  axis Unknown. 

Inclination  of  fygia  to  the  ecliptic. Unknown 


374  APPENDIX. 

A  pparent  diameter 2".4 

Diameter  in  miles 33,610 

Diameter  (earth's  being  1) ,.....' 4.719 

Volume  (earth's  being  1) 76.6 

Mass  or  weight  (earth's  being  1) 19.145 

Density  (earth's  being  1) 0.222 

Light  received  at  perihelion  (earth's  being  1) 0011 

Same  at  aphelion  (earth's  being  1) 0011 

"Weight  of  a  terrestrial  pound  or  gravity 1.36 

fallen  through  in  one  second  of  time,  in  feet 21.8 


ELEMENTS  OF  NEPTUNE'S  SATELLITES. 

No.1. 

Sidereal  revolution 6d  21h  2m  43s 

Longitude  of  the  ascending  node 175^  40' 

Longitude  of  perihelion 177°  30' 

Inclination  to  ecliptic 151°  0' 

Eccentricity 0.10597 


* 


ELEMENTS  OP  PERIODICAL  COMETS. 

HALLBT'S  COMET,  1835,  Nor.  15. 

Time  of  perihelion  passage 22h  41m  22a 

Longitude  of  perihelion .". 304°  31'  32" 

Longitude  of  the  ascending  node 55°  9'  59" 

Inclination  to  the  ecliptic 17°  45'  5" 

The  semi-axis 17.98796 

Eccentricity 0.967391 

Period  in  days 27,865d.74 

Retrograde 

ENCKE'S  COMET,  1845,  AUG.  9. 

Tune  of  perihelion  passage 15h  llm  11s 

Longitude  of  perihelion 157°  44'  21" 

Longitude  of  the  ascending  node 334°  19'  33" 

Inclination  to  the  ecliptic 13°  7'  34" 

The  semi-axis 2.21640 

Eccentricity 0.847436 

Period  in  days l,205d.23 

Direct.. 


APPENDIX.  375 

BIELA'S  COMET,  1846,  FEB.  11. 

Time  of  perihelion  passage Oh  2m  50a 

Longitude  of  perihelion. . .  t 109°  5'  47" 

Longitude  of  the  ascending  node 245°  56'  58" 

Inclination  to  the  ecliptic 12°  34'  14" 

The  semi-axis 3.50182 

Eccentricity 0.755471 

Period  hi  days 2,393d,52 

Direct 

PATE'S  COMET,  1843,  OCT.  17. 

Time  of  perihelion  passage 3h  42m  16s 

Longitude  of  perihelion ; 49°  34'  19" 

Longitude  of  the  ascending  node 209°  29'  19" 

Inclination  to  the  ecliptic 11°  22'  31" 

The  semi-axis 3.81179 

Eccentricity 0.555962 

Period  in  days 2,718d.26 

Direct 

DB  Vice's  COMET,  1844,  SEPT.  2, 

Time  of  perihelion  passage llh  36m  53a 

Longitude  of  perihelion 342°  31'  15" 

Longitude  of  the  ascending  node . .-. 63°  49'  31" 

Inclination  to  the  ecliptic 2°  54'  45" 

The  semi-axis 3.09946 

Eccentricity 0.617256 

Period  in  days l,993d.09 

Direct 

COMET,  1846,  FEB.  25. 

Tune  of  perihelion  passage 9h  13m  35s 

Longitude  of  perihelion 116°  28'  34" 

Longitude  of  the  ascending  node 102°  39'  36" 

Inclination  to  the  ecliptic 30°  55'  7" 

The  semi-axis 3.15021 

Eccentricity 0.793629 

Period  in  days 2,042d.24 

Direct.. 


•  This  comet  which  wu  oUerred  dotrtb  in  1*16  wu  still  divided  *t  ite  return 

In  1862. 


NOTE  TO  TEACHERS  AND  STUDENTS. 


THE  author,  as  an  old  teacher,  ventures  to  suggest  to 
the  teachers  and  students  who  may  adopt  this  volume  as 
a  text-hook  on  astronomy,  the  following  general  outline 
of  the  subjects  which  should  be  prepared  for  discussion. 

At  an  examination,  all  the  subordinate  parts  of  any 
one  subject  may  be  given  to  the  same  pupil,  while  at  a 
recitation  these  parts  may  be  divided  among  the  class,  in 
any  order  which  the  teacher  may  elect. 

Nearly  every  subject  may  be  illustrated  by  a  diagram, 
and  the  use  of  the  black-board  in  demonstration  is  now 
too  highly  appreciated  to  need  any  commendation. 

A  thorough  drilling  by  questions  can  alone  familiar- 
ize students  with  a  rapid  and  correct  use  of  the  technical 
language  of  any  science.  More  especially  is  it  necessary 
in  acquiring  a  perfect  knowledge  of  the  definitions. 

It  will  be  seen  that  the  reasoning  is  carried  as  far  as 
could  be  done  without  the  use  of  mathematics  ;  indeed,  it 
is  carried  up  to  the  point  where  the  processes  of  analysis 
come  in  to  give  quantities,  and  here  my  plan  compels  me 
to  stop. 


TOPICS  IN   "POPULAR  ASTRONOMY"   FOR 
DISCUSSION. 


I.— SUN'S  APPARENT  MOTION. 
This  subject  involves : 

1.  The  changes  in  the  points  at  which  the  sun  rises  and  sets.    The 
period  in  which  these  changes  are  accomplished.    The  seasons  and 
length  of  the  year. 

2.  The  sun's  movement  among  the  fixed  stars.    Diurnal  revolution 
of  the  stars  and  of  the  sun.    Altitude  of  the  sun's  meridian  passage. 
Explanation  of  the  use  of  the  gnomon  hi  determining  the  sun's  orbit 
and  the  inclination  of  the  equator  to  the  ecliptic. 

3.  The  variable  motion  of  the  sun  among  the  stars.    Period  from 
vernal  to  autumnal  equinox  compared  with  the  period  from  autumnal 
to  vernal  equinox.    How  the  inequality  of  these  periods  was  explained 
by  Hipparehus.    (Here  draw  the  figure  on  the  black-board,  and  make 
the  demonstration.) 

IL— SOLAB  ECLIPSES. 
*  This  subject  involves: 

1.  The  discovery  of  the  cause  producing  an  eclipse  of  the  sun.     The 
interposition  of  the  dark  body  of  the  moon. 

2.  Explain  why  a  solar  eclipse  does  not  occur  at  every  new  moon. 

3.  Show  how,  by  record  and  observation,  the  return  of  eclipses  was 
discovered  to  take  place  at  the  end  of  nineteen  years. 

4.  Show  what  phenomena  must  fall  together  to  produce  a  solar 
eclipse,  and  how  thought  combined  with  observation  might  have  pre- 
dicted the  coming  of  a  solar  eclipse. 

5.  Deductions  Iroin  the  discovery  of  the  true  cause  of  an  eclipse  of 
the  sun. 

HI.— THE  SOLAK  PARALLAX. 
This  subject  involves : 

1.  The  explanation  of  parallax  and  the  mode  of  measuring  the  dis- 
tance of  inaccessible  objects  on  the  earth. 

2.  Why  this  method  is  not  applicable  to  the  measure  of  the  sun's 
distance. 

3.  Draw  the  figure  and  demonstrate  the  method  of  deducing  the 
solar  parallax  from  the  transit  of  Venus. 

4.  Deduce  the  sun's  real  magnitude  from  his  distance  and  apparent 
diameter. 

IV.— THE  SUN'S  PHYSICAL  CONSTITUTION. 
This  subject  embraces : 

1.  An  explanation  of  the  solar  spots.    Their  magnitude,  outline,  and 
periodical  changes. 

2.  The  deduction  of  the  sun's  period  of  rotation  and  the  position  of 
his  ftyig. 


378  TOPICS  FOR  DISCUSSION. 


3.  The  measurement  of  the  intensity  of  the  solar  heat,  and  specula- 
tions as  to  ite  production. 

4.  The  sun's  atmosphere,  and  the  red  flames  seen  during  a  total 
eclipse. 

6.  The  zodiacal  light 

V.— THE  PLANET  MERCURY. 
This  subject  involves : 

1.  The  discovery  of  the  planet.    Its  elongations,  motions,  and  retro- 
gradations. 

2.  Explain  these  phenomena  by  a  circular  orbit  for  Mercury,  and  an 
eccentric  position  for  the  sun. 

3.  Explain  the  transits  of  Mercury,  and  deduce  the  inclination  of 
Mercury's  orbit  to  the  ecliptic. 

4.  Determine  the  distance  of  Mercury  from  the  sun,  knowing  the 
earth's  distance. 

6.  Illustrate  the  advance  in  astronomical  accuracy  from  the  predic- 
tions of  the  transits  of  Mercury. 

6.  Deduce  the  actual  diameter  of  Mercury. 

VI.— THE  PLANET  VENUS. 

This  subject  involves  the  same  discussion  as  the  preceding. 

VIL— THE  EARTH'S  POSITION. 
This  subject  embraces : 

1.  The  earth's  position  as  determined  by  the  senses. 

2.  The  same,  as  deduced  from  the  solar  and  lunar  motions. 

3.  The  system  of  Hipparchus  enlarged  by  Ptolemy. 

4.  Causes  which  led  Copernicus  to  abandon  the  Ptolemaic  system. 
The  Copernican  system. 

VI1L— THE  FIGURE  AND  MAGNITUDE  OF  THE  EARTH. 

Under  this  head  discuss: 

1.  The  earth's  figure,  as  deduced  from  simple  observation. 

2.  Show  how  the  circumference  of  the  earth  may  be  measured,  and 
the  diameter  deduced. 

IX.— THE  MOTIONS  OF  THE  EARTH. 

Here  discuss: 

1.  The  diurnal  revolution  of  the  earth.    A  measure  of  time.    The 
velocity  uniform. 

2.  The  revolution  of  the  earth  in  its  orbit.    Inclination  of  the  earth's 
axis.    Show  how  the  seasons  are  produced,  and  the  changes  of  inclina- 
tion of  the  equator  to  the  ecliptic. 

3.  Explain  the  anomalistic,  tropical,  and  sidereal  years. 

4.  Discuss  the  motion  oi  the  perihelion  of  the  earth's  orbit. 
6.  Solar  and  sidereal  time. 

X.— THE  MOON. 
Examine : 

1.  The  moon's  movement  among  the  fixed  stars. 

2.  Explain  the  moon's  phases. 

3.  The  cause  of  a  lunar  eclipse.    The  phenomena  then  witnessed. 


TOPICS  FOR  DISCUSSION.  379 

4.  The  moon's  rotation  on  her  axis.    Its  period  and  consequences. 

5.  Motion  of  the  perigee  of  the  moon's  orbit    How  explained  by 
Hipparchus. 

6.  Inclination  of  the  moon's  orbit 

XL— THE  LUNAR  PARALLAX  AND  DISTANCE. 

Explain  here : 

1.  The  subject  of  parallax  as  hi  No.  IIL,  and  apply  to  the  moon. 

2.  Deduce  the  moon's  actual  diameter  from  her  distance  and  appar- 
ent diameter. 

XIL— THE  SURFACE  OP  THE  MOON. 
State  generally: 

1.  What  irregularities  of  surface  are  shown  by  the  telescope? 

2.  The  outline  of  the  illuminated  portion,  the  mountain  tops  and 
shadows. 

3.  The  lunar  cavities.    Their  depths.    How  measured. 

4.  Imagined  seas  and  rivers  on  the  moon.     Supposed  volcanoes. 
6.  The  lunar  atmosphere  inappreciable,  or  nearly  so. 

XIIL— THE  MOON'S  CENTER  OP  FIGURE. 

State  the  facts  and  exhibit  the  results  of  a  non-coincidence  of  the 
centers  of  figure  and  of  gravity. 

XIV.— THE  PLANET  MARS  AND  HIS  MOTIONS. 
This  subject  involves: 

1.  A  presentation  of  the  facts  with  reference  to  the  planet    Hia 
revolution  among  the  stars.     His  stations,  advances,  and  retrograda- 
tions.     His  great  increase  and  decrease  hi  magnitude. 

2.  The  Ptolemaic  explanation  of  these  facts.    (Use  the  figure,  page 
103.) 

3.  State  Kepler's  plan  of  investigation,  and  the  limit  of  error  on 
which  ho  proposed  to  reconstruct  astronomy. 

XV.— KEPLER'S  LAWS. 

1.  Show  how  Kepler  proved  that  no  combination  of  circular  motion 
would  explain  the  phenomena  exhibited  by  Mars. 

2.  Draw  the  figure  (page  108)  and  explain  the  chief  properties  of 
the  ellipse. 

3.  Explain  the  steps  which  led  to  the  discovery  of  the  first  law,  and 
give  the  law. 

4.  Explain  the  second  law. 

5.  Show  how  an  ellipse  is  determined  hi  magnitude,  in  position  on 
its  own  plane,  and  how  the  position  of  its  plane  is  obtained. 

6.  Show  how  Kepler  reached  his  third  law.     State  the  law  and  its 
value. 

XVI.— PHYSICAL  CONSTITUTION  OF  MARS. 
This  subject  embraces : 

1.  An  explanation  of  the  changes  in  the  apparent  diameter  of 
Mars. 

2.  A  general  account  of  its  mirface.  as  shown  by  the  telescope. 
3    The  determination  of  its  period  of  rotation. 


380  TOPICS  FOR  DISCUSSION. 

4.  The  inclination  of  its  axis  and  its  seasons. 

5.  General  resemblance  to  the  earth. 

XVIL— THE  DISCOVERT  OF  CEEES  AND  THE  ASTEROIDS. 
Present : 

1.  The  reasons  for  suspecting  the  existence  of  a  planet  between  Mara 
and  Jupiter. 

2.  Explain  Bode's  law. 

3.  State  the  facts  of  the  association  formed  to  search  for  the  supposed 
planet,  and  the  mode  of  research. 

4.  Give  the  circumstances  of  the  loss  and  re-discovery  of  Ceres. 

5.  General  facts  of  the  discovery  of  the  other  Asteroids.     (For  num- 
ber, names,  elements,  etc.,  see  Appendix.) 

XVIIL— MOTIONS  OF  JUPITER. 
Discuss  the  subject,  as  follows : 

1.  Show  by  figure  (page  135)  how  the  planet  appears  to  retrograde. 

2.  By  figure  (page  136),  explain  the  stationary  points. 

3.  Show  how  to  obtain  the  distance  of  Jupiter  from  the  Sun,  in  terms 
of  the  Earth's  distance,  by  measuring  the  arc  of  retrogradation  hi  24 
hours.    (Figure,  page  137.) 

4.  Deduce  the  Sidereal  Revolution  from  the  Observed  Yalue  of  the 
Synodical  Revolution. 

XIX.— PHYSICAL  CONSTITUTION  OF  JUPITER. 

1.  Give  the  appearance  of  the  planet  as  seen  in  the  telescope. 

2.  Show  how  the  period  of  rotation  on  its  axis  is  obtained. 

3.  Explain  how.the  actual  diameter  is  derived  from  the  distance  and 
apparent  diameter. 

XX.— JUPITER'S  MOONS. 

1.  The  history  of  their  discovery.    Effect  on  the  Copernician  doctrine. 

2.  Nature  of  their  orbits.-    Elongations.    Transits.    Eclipses. 

3.  Uses  in  the  determination  of  terrestrial  longitude.    (Here  explain 
the  terms  longitude  and  latitude,  and  the  importance  of  their  accurate 
determination  to  navigation.) 

4.  Show  how  the  eclipses  of  Jupiter's  satellites  may  be  used  in  meas- 
uring the  velocity  of  light. 

XXL— THE  SYSTEM  OF  SATURN. 

1.  Facts  known  before  the  telescope  was  applied. 

2.  Illustrate  the  advance  of  the  telescope  in  optical  power,  by  stating 
the  successive  discoveries  of  the  rings  of  Saturn. 

3.  Explain  the  cause  of  the  disappearance  of  the  rings,  and  the  phe- 
nomena generally. 

4.  Give  some  of  the  principal  dimensions  of  the  rings. 

5.  State  the  general  facts  with  reference  to  the  satellites.    (See  Ele- 
ments, Appendix,  pages  372  and  373.) 

XXII.— TRANSITION  FROM  FORMAL  TO  PHYSICAL  ASTRONOMY. 

1.  Show  how  increased  accuracy  of  observation  gradually  produced  and 
modified  the  systems  of  Hipparchus,  Ptolemy,  Copernicus,  and  Kepler. 

2.  Explain  the  difference  between  formal  and  physical  Astronomy. 


TOPICS    FOB    DISCUSSION.  381 


3.  Give  the  facts  of  formal  Astronomy. 

4.  Present  the  demands  of  physical  Astronomy. 

XXIIL— LAWS  OP  MOTION. 
This  subject  embraces : 

1.  An  exhibition  of  the  views  entertained  by  the  followers  of  Ara- 
totle  and  the  ancients. 

2.  Kepler's  opinions. 

3.  Galileo's  investigations  and  discovery  of  the  first  law  of  motion, 

4.  The  discussion  of  the  second  law  of  motion. 
6.  The  third  law  of  motion. 

XXIV.— DISCOVERT  OP  THE  LAW  OP  GRAVITATION. 

Discuss  this  subject,  as  follows : 

1.  The  views  of  Kepler  and  his  successors  as  to  the  necessity  of  a 
physical  theory  of  planetary  motion. 

2.  The  law  of  the  centrifugal  force. 

3.  Borelli's  suggestions. 

4.  Newtou's  five  steps  in  the  discussion. 

XXV.— NEWTON'S  DEMONSTRATION  OP  THE  LAW  OF  UNIVERSAL 
GRAVITATION. 

1.  Measure  of  the  intensity  of  any  force. 

2.  Experiment  of  dropping  a  heavy  body  at  different  distances  from 
the  earth. 

3.  The  moon  employed  as  the  falling  body,  and  results  reached. 

4.  Extension  of  the  law  of  gravitation  as  existing  in  the  earth  to  the 
other  heavenly  bodies. 

5.  Same  law  extended  to  every  particle  of  the  earth  and  in  the  universe. 

XXVL— A  SYSTEM  OP  TWO  BODIES. 

1.  Show  what  five  quantities  are  required  by  the  mathematician  to 
trace  a  single  planet. 

2.  Trace  out  the  circumstances  of  motion  of  the  planet,  and  show 
their  perpetual  repetition. 

3.  Explain  how  a  perfect  equilibrium  might  have  been  secured  by 
using  different  kinds  of  matter. 

XXVII.— A  SYSTEM  OF  THREE  BODIES. 
Involves  a  discussion  of: 

1.  The  earth  as  fixed,  the  moon  as  disturbed  by  the  sun.    The  sun'a 
center  in  the  prolongation  of  the  axis  of  the  moon's  orbit. 

2.  Same  circumstances,  only  the  sun  to  revolve  by  successive  advances. 

3.  Same  with  the  sun  revolving  uniformly. 

4.  Consider  the  changes  produced  by  giving  to  the  moon's  orbit  an 
inclination  to  the  ecliptic. 

XXVIII.— A   SYSTEM   OF   THREE   BODIES.— THE   DISTUBING  BODY 
BEING  A  PLANET. 

1.  Apply  the  reasoning  in  XXVIL  to  this  case. 

2.  State  the  complexity  and  the  necessary  use  of  the  highest  math- 
ematics. 


382  TOPICS    FOB    DISCUSSION. 


XXIX.— WEIGH   THE   SUN,  THE  EARTH'S  "WEIGHT  BEING  TAKEN 
AS  THE  UNIT. 

1.  Show  that  the  velocity  impressed  on  a  falling  body  in  a  unit  of  time 
at  a  unit's  distance,  measures  the  weight  of  the  attracting  body. 

2.  Use  the  moon  as  the  body  falling  to  the  earth,  and  the  earth  aa 
the  body  falling  to  the  sun. 

3.  Show  how  instruments  are  required  to  make  the  measures  de- 
manded in  this  problem. 

XXX.— TO    OBTAIN  THE  WEIGHT   OF    A  PLANET,  OE  SATELLITE, 
IN  TERMS  OF  THE  EARTH'S   WEIGHT. 

1.  Show  how  to  weigh  a  planet  having  a  satellite. 

2.  Explain  how  the  weight  of  a  planet  having  no  satellite  is  obtained. 

3.  Show  how  the  weights  of  the  satellites  are  obtained. 

XXXL— THE  TRANSIT  INSTRUMENT,  ITS  USES  AND  ERRORS. 

1.  Explain  the  structure  of  the  instrument.     The  tube,  or  telescope. 
Line  of  culmination.     Horizontal  axis  and  pivots,  etc. 

2.  The  errors  of  position.     Of  pivots.     Of  clock.     Of  observer.     Pre- 
cession.    Nutation.     Aberration,  etc. 

3.  Explain  the  old  method  of  observation,  and  the  American  method 
of  electro- magnetic  record. 

XXXIL— THE   MURAL  AND  MERDIAN   CIRCLE. 

1.  North  polar  distance,  how  determined. 

2.  Flexure  of  tube.     Form  of  pivots.     Errors  of  division  on  the 
circle,  etc. 

3.  The  screw  micrometer.     Its  construction  and  use. 

4.  The  declinometer,  as  a  means  of  measuring  differences  of  north 
polar  distance. 

XXXIII.— THE  EQUATORIAL  TELESCOPE. 

1.  Reflecting  instruments. 

2.  Refracting  telescopes. 

3.  Space  penetrating  power. 

4.  Defining  power. 

5.  General  structure  of  the  equatorial. 

XXXIV.-THE  PLANET  UEANUS. 

1.  The  history  of  its  discovery. 

2.  The  figure  and  magnitude  of  the  planet. 

3.  The  satellites. 

4.  The  disagreement  between  observation  and  computation  leads  to 
the  discovery  of  Neptune. 

XXXY.— THE  DISCOVERT  OF  NEW  PLANETS. 

1.  Discovery  by  accident,  as  that  of  Uranus,  by  Sir  "W.  HerscheL 

2.  Discovery  by  research,  as  that  of  Ceres,  by  Piazzi. 

3.  Discovery  by  computation  based  on  observation,  aa  that  of  Ceres 
te-discovered  by  Gauss. 

4.  Discovery  by  perturbative  effects,  as  that  of  Neptune. 


TOPICS    FOB    DISCUSSION.  383 


XXXVI.— DISCOVERY  OP  NEPTUNE. 
In  this  discussion,  show : 

1.  What  is  meant  by  the  normal  figure  of  the  elliptic  orbit  of  Uranus. 

2.  How  this  figure,  being  disturbed,  would  lead  to  a  knowledge  of 
the  place  of  the  disturber. 

3.  Give  the  true  case  of  nature  as  to  the  orbit  of  Uranus,  and  how 
the  normal  orbit  must  be  reached  by  approximation. 

4.  Show  how  the  limits  of  research  may  be  reduced.    The  disturber 
revolves,  probably,  near  the  plane  of  the  ecliptic.     Obeys,  probably, 
Bode's  law  as  to  distance.    Hence,  its  probable  periodic  time.    Place 
indicated  roughly  by  maximum  effect.     (Use  figure,  page  273.) 

5.  Explain  how  large  errors  in  the  computed  elements  did  not  pre- 
vent the  discovery  of  the  unknown  planet 

XXXVIL— THE  CONIC  SECTIONS. 

1.  Announce  the  reverse  problem  of  gravitation  (page  283). 

2.  Use  figure,  page  284,  in  explaining  the  curves,  which  may  be  cut 
by  a  plane  from  a  conic  surface,  viz.,  the  circle,  parabola,  ellipse,  and 
hyperbola. 

XXXVIIL— GRAVITY  APPLIED  TO  THE    MOTIONS   OF  COMETS. 

1.  Notice  the  comet  of  1680. 

2.  Halley's  comet  of  1682.   Give  the  history  of  Halley's  investigations, 
and  of  his  prediction  of  its  return  hi  1759. 

3.  Computation  of  Clairault  and  associates,  and  error  of  prediction. 

4.  Return  in  1835. 

XXXIX— PHYSICAL  CONSTITUTION  OF  COMETS. 

1.  Describe  the  nucleus,  or  the  head.    The  envelope.    The  tafl. 

2.  The  phenomena  in  the  envelope,  and  in  the  tail. 
4.  Encke's  comet,  and  Bela's  double  comet. 

4.  Give  Herschel's  conclusions,  page  298. 

5.  Xotice  the  probable  number  of  comets. 

XK— STABILITY  OF  THE  PLANETARY  SYSTEM. 
This  subject  may  be  divided  thus: 

1.  Specify  and  define  the  elements  of  a  planet's  orbit. 

2.  Specify  the  elements  on  which  the  well-being  of  a  planet  depends. 

3.  Show  the  stability  of  the  inclinations.    (Use  figure,  page  305.) 

4.  Show  the  changes  in  the  line  of  nodes. 

5.  Demonstrate  the  stability  of  the  major  axes. 

6.  Consider  the  effect  of  the  normal  component  of  the  disturbing 
force. 

XLI.— THE  SUN  CONSIDERED  AS  A  HEAVY  BODY. 

1.  Show  the  real  diameter  of  the  sun. 

2.  Find  the  mass  of  the  sun  in  terms  of  the  earth's  mass. 

3.  Find  the  specific  gravity  of  the  sun. 

4.  Show  how  much  a  pound  on  the  earth's  equator  would  weigh  on 
the  sun. 

5.  Compute  the  space  through  which  a  heavy  body  would  fall  in  one 
uecond  at  the  sun's  equator. 


884  TOPICS    FOB    DISCUSSION. 


XLII.— MERCURY  CONSIDERED  AS  A  HEAVY  BODY. 
L  Show  how  the  planet's  weight  may  be  obtained. 

2.  Deduce  the  specific  gravity. 

3.  Show  what  changes  are  progressing  in  the  elements  of  the  orbit, 
(See  Appendix,  for  Elements.) 

4.  Compute  the  sun's  power  on  Mercury  in  aphelion,  as  compared 
with  its  power  in  perihelion. 

5.  Compute  the  relative  power  of  the  sun,  of  Tenus,  and  of  the 
earth,  over  Mercury,  all  the  planets  being  in  conjunction. 

6.  Compute  the  power  exerted  on  Mercury  by  the  planet  Jupiter. 

XLIH.— VENUS  AS  A  PONDERABLE  BODY. 

1.  Same  as  in  XLII. 

2.  Consider  the  effect  of  near  commensurability  in  the  periods  of 
Venus  and  the  earth. 

XLIV.— THE  EARTH  AS  A  PONDERABLE  BODY. 

1.  Same  as  XLII. 

2.  Show  how  the  earth's  weight  in  pounds  may  bo  obtained. 

3.  Explain  the  figure  of  the  earth. 

4.  Discuss  the  equilibrium  of  the  ocean. 

5.  Explain  the  subject  of  precession. 

6.  Discuss  the  subject  of  nutation. 

7.  Explain  the  acceleration  of  the  moon's  mean  motion. 

XLV.— MARS  AS  A  PONDERABLE  BODY. 

1.  Show  the  figure  of  the  orbit  of  Mars,  and  examine  the  sun'a 
power  on  Mars  in  Various  points  of  his  orbit. 

2.  Explain  why  Mars  was  well  selected  by  Kepler. 

3.  Same  as  in  XLII. 

The  remaining  planets  may  be  discussed  and  examined  as  to  the  fol- 
lowing points: 

1.  The  real  diameter. 

2.  The  mass,  or  weight. 

3.  The  velocity  of  felling  bodies  on  their  equators. 

4.  The  weight  of  a  terrestrial  pound  on  the  equator  of  the  planet. 

5.  Compute  the  power  of  the  planet  next  interior,  and  also  of  the 
one  next  exterior,  and  compare  the  same  with  the  power  of  the  sun. 

6.  Consider  the  planets  with  reference  to  the  effect  of  a  near  com- 
mensurability  of  the  periodic  times. 

XLVI.— THE  NEBULAR  HYPOTHESIS. 

Discusa  the  subject  in  the  order  laid  down  in  the  heading  of  the 
chapter. 


14  DAY  USE 

IETURN  TO  DESK  FROM  WHICH  BORROWED 

LOAN  DEPT. 

This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 
Renewed  books  are  subject  to  immediate  recall. 


19681 


LOAN  DEPT,, 

QCT27196865. 


HUM  I  i  'bb  •'* 


RECDLD    MAR 


LD  2lA-10m-l,'68 
(H7452slO)476B 


5'72  -3PM  56 


General  Library 

University  of  California 

Berkeley 


